Showing papers in "Journal De Physique Lettres in 1982"

Density of states on fractals : « fractons »

Abstract: The density of states on a fractal is calculated taking into account the scaling properties of both the volume and the connectivity. We use a Green's function method developed elsewhere which utilizes a relationship to the diffusion problem. It is found that proper mode counting requires a reciprocal space with new intrinsic fracton dimensionality d = 2 d/(2 + δ). Here, d is the effective dimensionality, and δ the exponent giving the dependence of the diffusion constant on distance. For example, we find for percolation clusters d = 4/3 within the numerical accuracy available, independent of the Euclidean dimensionality d. Crossover to normal behaviour at low frequencies is discussed for finite fractals and for percolation above the percolation threshold pc. Relevance to experimental results on proteins is also discussed.

Period doubling cascade in mercury, a quantitative measurement

Abstract: 2014 Observation of the period doubling cascade in a Rayleigh-Bénard experiment in mercury. The experimental cell has an aspect ratio 0393 = 4 and contains four convective rolls. A DC magnetic field of 270 G is applied along the convective roll axis. The measured Feigenbaum number is 03B4 = 4.4. The ratio of the successive subharmonics is of the order of 14 dB for the lowest measured subharmonics. Tome43 No 7 1 er AVRIL 1982 LE JOURNAL DE PHYSIQUE LETTRES J. Physique LETTRES 43 (1982) L-211 L-216 ler AVRIL 1982, Classification Physics Abstracts 47.20 47.65 The period doubling cascade as a route to chaos is now well documented theoretically [1] ] as well as experimentally [2]. We present here new results on a Rayleigh-Benard experiment in a cell of liquid mercury with an aspect ratio larger than in previously reported works on helium or water (four convective rolls). The very good signal to noise ratio of the experiment allows a precise determination of the Feigenbaum number and of the power ratio of the successive subharmonics. In this experiment, a DC magnetic field, applied along the convective roll axis, introduces an extra damping of the oscillators which favours the period doubling cascade. 1. An experimental dynamical system with controlled dissipation. At low Prandtl number, the relevant instability of two-dimensional convective rolls, which leads to time dependent convection and chaos, is the oscillatory instability [3]. It was shown [2] in experiments of convection in liquid helium that for a range of Prandtl numbers and wavenumbers of the convective pattern, one route to chaos is a period doubling cascade, which follows the Feigenbaum scenario [1]. It is customary to compare this type of experiments to a one-dimensional mapping. But this mapping relates to strongly dissipative modes. A more realistic mapping is therefore a two-dimensional one with two parameters, a constraint and a viscosity (area contraction in phase space). The Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:01982004307021100 L-212 JOURNAL DE PHYSIQUE LETTRES simplest quadratic one is the Henon mapping [4] which reduces for infinite contraction to a onedimensional mapping. In a way, we want to find a physical system depending on those two parameters. In a Rayleigh-Benard experiment, the constraint is the Rayleigh number R. At low Prandtl number, the damping of the modes associated with the oscillatory instability depends on the Prandtl number and the wavenumber of the convective pattern [3]. But it is not easy to control such parameters experimentally, and furthermore, they do not affect selectively the oscillatory instability. On the contrary, a horizontal magnetic field, parallel to the convective roll axis, will add a quantitative damping to the oscillatory instability, as we have recently shown [5]. This increased damping of the oscillators will favour the period doubling cascade as a route to chaos [6]. 2. Experimental apparatus. Our experimental system has been described in detail elsewhere [5, 7]. We use a parallelepipedic cell of aspect ratio r = 4 (dimensions 7 x 7 x 28 mm) with, in the convective state, four rolls parallel to the shorter side wall (see reference five for visualization). The top and bottom boundaries consist of two thick copper plates. The lateral boundaries are made of plexiglass. In the centre of the bottom plate, a small NTC (negative temperature coefficient) thermistor is located on a 2 mm diameter hole and is adjacent to the convective fluid. The temperature signal, given by the bolometer, is analysed by a 5 420 A H. P. digital analyser. An Fig. 1. Effect of a magnetic field parallel to the roll axis. The Rayleigh number is RI Rc = 2.9 at zero field. The two oscillators are locked (f1/12 = 2), the amplitude of oscillator 11 about 20 dB larger than the amplitude of oscillator f2 for H = 0. As H increases, the two oscillators tend to the same amplitude and keep their locking ratio 2. L-213 PERIOD DOUBLING CASCADE IN MERCURY electromagnet provides a uniform horizontal magnetic field. The experimental convective cell is placed in a vacuum chamber. 3. Effect of a DC magnetic field, parallel to the roll axis, on the oscillating state. Defining the Rayleigh number for the onset of convection as Rc, the first time dependent instability observed is the oscillatory instability, its onset being at R ^_r 2 Rc. As previously reported [7], the frequency of the oscillatory mode increases linearly with the Rayleigh number. It allows, by measuring the frequency, a precise determination of each bifurcation point Increasing slightly the Rayleigh number, a second frequency f2 appears in the temperature spectrum which, within a very small range of R, locks with fi, the ratio being it = 2 f2. We then apply a DC magnetic field parallel to the roll axis up to a field of 270 G. We present, in figure 1, the effect of the magnetic field on the direct local temperature recording. Two distinct regimes appear. 4 For H > 100 G, the evolution is the one described in our previous study [5]. The frequency of the oscillatory instability increases and so does the damping of the mode. This will tend at a higher field to a complete inhibition of the oscillatory instability. But for H 100 G, and the effect is already noticeable around 10 G, the relative oscillating strength of the two locked oscillators changes. This sensitivity to a very small field is surprising. Fig. 2. Direct time recordings of temperature for various stages of the period doubling cascade showing the onset of fl4 (R/R~ = 3.52), f/8 (RI Rc = 3.62), fl 16 (RI Rc = 3.65). L-214 JOURNAL DE PHYSIQUE LETTRES Fig. 3. The Fourier spectrum. Arrows indicate the peak at the frequency fl. The net result of this phenomenon is that, at 270 G, the two modes are highly damped and have about the same oscillating strength, whereas at zero field the mode f has an amplitude about 20 dB larger than the mode f ’r2. 4. The period doubling cascade. From now on, we keep a constant magnetic field H = 270 G. A typical recording is shown in figure 2 for ~//?c == 3.47. Let us note that it shows a striking similarity with a recent Cray machine simulation done by Upson et al. [8] on a Rayleigh-Bénard experiment in a small box. The corresponding Fourier spectrum is shown in figure 3A. As we increase the Rayleigh number, a period doubling cascade develops up to f/32, well resolved as far as the onset values up to fl 16. In table I, we present the various onset values of the cascade of pitchfork bifurcations. In figure 2, the temperature recordings are presented, showing the development of the subharmonics fl4, f/8 and ~/16, for R/ Rc = 3.52, 3.62 and 3.65. Their respective Fourier spectra are presented in figures 3B, C, D for values of ~/~c close to the preceding ones.

Competing structural orderings and transitions to glass in mixed crystals of Rb1-x(NH4)xH 2PO4

Abstract: Frustration is produced in crystals of the KDP family by mixing ferroelectric and antiferroelectric constituents. Birefringence and dielectric measurements are reported for 0 ≤ x ≲ 0.35. They indicate an interesting phase diagram, with a glassy phase probably preceded by a mixed phase for the upper part of the concentration range investigated. The randomness of the competing short-range interactions is likely to play a major role, making these structural glasses truly analogous to magnetic spin glasses.

Observation of a magnetic state in the organic superconductor (TMTSF) 2ClO4 : influence of the cooling rate

Abstract: A magnetic state is observed below ∼ 3.5 K in the organic superconductor (TMTSF)2ClO4 just above the superconducting transition (Tc ∼ 1 K). This state is obtained by fast cooling with a rate of ∼ 25 K/min. and evidenced by 77Se and 1H-NMR intensity and relaxation measurements. The onset temperature is nearly field-independent between 10 and 65 kOe. In the same sample, slow cooling suppresses the magnetism to at least below 1.3 K. The heat cycle effects are fully reproducible. The results imply that fast cooling freezes in lattice disorder which depresses superconductivity and therefore leave room for the competing magnetic phase. A small hydrostatic pressure also depresses the magnetism

Emergence of a periodic mode in the so-called turbulent region in a circular Couette flow

Abstract: 2014 The transition to turbulence is studied in normal fluid He contained between concentric cylinders with the inner cylinder rotating, for high Reynolds numbers R up to 500 Rc (Rc is the critical Reynolds number for the Taylor instability) and for small aspect ratios 0393 (0393 = l/d = fluid height/gap between cylinders). For sufficiently high values of d and in a range of R where the flow is considered as turbulent, a periodic mode appears and remains up to the maximum value of R. The Tand d-dependence of the mode has been studied. We suggest that this mode is related to a change in a boundary layers structure. J. Physique LETTRES 43 (1982) L-5 L-10 Classification Physics Abstracts 47.20 47.25F ler JANVIER 1982, Circular Couette flows are presently, with Rayleigh-Benard experiments, among the important experiments to study the successive instabilities, which appear in the transition from laminar to turbulent flow [1, 2]. In Couette flow, with the inner cylinder only rotating at the rotation rate Q, the steady flow is laminar for low values of ~2; for the critical value of the rotation rate Qc and the corresponding Reynolds number Rc = Dc R1 1 d/ v (v is the kinematic viscosity, R l, R2 are respectively the inner and outer cylinder radii, d = R2 R1), this flow becomes unstable and a new steady pattern of toroidal rings, the Taylor vortices, superimposed on the azimuthal laminar flow, is established. Then, the flow becomes time-dependent and the Taylor structure acquires azimuthal waves, which correspond to a single sharp frequency component 11 in the velocity spectrum. For larger values of ~(~/~e = ~/~e ~ 10), a second frequency component f2 Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019820043010500 L-6 JOURNAL DE PHYSIQUE LETTRES appears [3]. For R/ R~ ^~ 12, a broadband component centred at fB = 0.4 Q becomes apparent, this latter component is the only one which remains for /~/~ ~ 20 and appears as the signature of the turbulent flow [2]. For still larger values of R and particular experimental conditions, Walden and Donnelly [4] have found a new sharp peak fr, which reemerges in the power spectrum. Barcilon et al. [5] and Koschmieder [6] have studied the turbulent flow for high values of R (~ 200-300 R~) and have observed through a visualization technique the appearance of a smaller scale structure, attributed to Gortler vortices by Barcilon et al. The low value of the kinematic viscosity of normal helium (v = illp = 2 x 10-4 cm2 . s-1 i.e. two orders of magnitude lower than usual liquids) permits us to study easily its hydrodynamic behaviour at very high values of ~(~ 500 Rc) with the experimentally imposed mechanical parameters of rotation (d, R1 and 92). Thus, the described results concern particularly the range of rotation which corresponds to the usually called « turbulent state ». As soon as d is sufficiently large (d/R > 0.08), the more striking result is the formation of a new ordered structure, characteI rized by a sharply defined periodic mode « R » similar to the « wavy mode ». 1. Experimental procedure. The experimental apparatus consists of two concentric cylinders : the radius of the stator is R2 = 2.650 cm ± 0.001 cm and the radius of the rotor R1 can be chosen between 2.55 cm to 2.15 cm. For all values of d, the aspect ratio r =1/d (1= cylinder height) can be taken between 2 and 12. In rotation experiments at liquid helium temperature, obtaining a stable rotation with a small dissipation is difficult; with our apparatus, the rotation rate f2 is constant to better than ± 0.3 % in the range 10-1-10 Hz with the gap d constant to better than ± 3 p whatever the rotation ~2. But the main difficulty is to assume a constant temperature of the helium liquid in the studied range To = 2.2 K-3 K (1 mK corresponds to the threshold difference of temperature for Rayleigh-Benard instabilities in helium liquid with a characteristic length of 2 mm). To obtain this temperature stability, we control the main He bath to within 10-2 K by the regulation of the vapour pressure of liquid He with a mechanical manostat ; a stainless steel chamber partially isolates the experimental cell from the main bath; the two cylinders are made in copper, and the stator is electronically regulated at a constant temperature T 1 = To + e(e ~ 3 x 102 K to within 10-6 K); the temperature of the liquid helium between the cylinders is thus maintained at the temperature T with a stability better than 103 K. The detection system, somewhat different from the one used in preliminary results [7], is similar to the method used in hot wire anemometry : the detector is an Aquadag painted layer with a rectangular form (~1x5 mm), the larger dimension being parallel to the azimuthal flow, so that it is more sensitive to the departure from this main flow; it is heated by a d.c. power of typically 10S W, such that its stationary temperature at 0 = 0 is greater than the liquid one T1 by about 103 K. When 0 differs from 0, the heat of the probe is more and less scattered by the flow, therefore its temperature and resistance value r depend on the local velocity field. We measure the detector resistance using a lock-in detector and an a.c. bridge; the bridge signal proportional to is analysed using a HP 5420 A digital signal analyser. It is difficult to estimate the size of the probed volume, but we think that it expands on a radial dimension of about 1 mm ; thus by no means can the probe be considered as testing the boundary layer only. This detection allows us to reach experimentally the threshold Dc of the onset of the Taylor cells : these thresholds are determined by a small jump br(t ) and the apparition of low frequency oscillations of the probe resistance; the determined values Qcexp = 12 mHz for d = 2 mm and S2~ ~Xp = 35 mHz for d = 1 mm correspond to a mean critical Taylor number L-7 TURBULENCE IN CIRCULAR COUETTE FLOW this value is 20 % higher than the theoretical one (Tac = 3 370). All the reported results will be given as a function of the dimensionless measure of the rotation rate TalTa,,, or R/Rc. 2. Experimental results. 2.1 MODES «B» AND « R ~. 2013 Let us now describe the evolution of the time dependence of the local velocity by the study of r(t) and the corresponding power spectrum P( f ) as R is increased, for r = 6 and d = 2 mm (Fig. 1). For values of R from 6 Rc to 10 Rc a mode is present, the frequency component of its velocity spectrum is broad and centred around fB ~ 0.4 92; its features (appearance, broadband, value) are similar to the mode « B » seen in usual liquids after the sharp modes f1 and f2 [2], but it seems more important in our case; this mode persists up to R = 39 R~, although its behaviour changes with increasing Q : gradually, high order harmonics of fB appear and their amplitude is no longer decreasing but show a maximum around the seventh harmonic (Fig. lb). In figure lc, for R/Rc = 37, the fundamental mode Fig. 1. Frequency spectrum P(f) of the detector time-dependent resistance r(t) for increasing normalized Reynolds numbers R/Re The abscisse scale is normalized to the rotation rate 0 for each spectrum and a logarithmic scale with arbitrary units is used for the vertical axis. Figures 1 a, 1 b, Ic are related to the mode « B » for R/R~ = 7, 11, 37 (frequency fB and its harmonics). In figure ld (R/Rc = 116), the sharp frequency components f R and f 2 R characterize the mode « R » ; the modulation mode fm is not easily seen in this figure. In all recordings, d = 2 mm, R2 = 26.5 mm, r = 6 and T ~ 2.4 K. L-8 JOURNAL DE PHYSIQUE LETTRES fB is always important, but only the 6th and 7th harmonics remain and are sharper [8]. For R = RR = 39 Rc, an abrupt transition occurs, the mode « B » and its harmonics disappear, the velocity spectrum is only dominated by the sharp frequency component fR and the harmonic 2 fR, 3 fR of a mode which we label « R » ; this mode remains for values of R/R~ from 39 to the maximum rotation rate (R/jRc ~ 500) and corresponds to the power spectrum recorded in figure ld (R/Rc = 116). Let us note at this point that the change in the background noise is not relevant [9]. Let us describe the main features of this mode « R » : : Its observation for 0 > S2R does not depend on previous history. As for the « wavy » modes fl [10], it can exist in many states so that its frequency fR can be written fR = nFR with generally 3 n 6 (n = 5, 6 are the most probable modes). All the experimental results are summarized in figure 2, where we have plotted the 0-normalized frequency as a fonction of the Qc-normalized rotation rate for r = 6 and d = 2 mm; we see that for ~/~c ~ 150, n is not single valued and its value depends mainly how the rotation rate is established. For R/R~ ~ 150, the ratio fR/nQ is nearly constant (in Fig. 2, ~/~2 = 0.38). Often, this mode is slightly modulated at a frequency fm close in value to fB ; this modulation corresponds in the velocity spectrum to two broad peaks at frequencies fR ± fm. We have plotted in figure 2 the Q-dependence of this modulation mode fm ; for large values of R/R~, this modulation is more effective and a frequency locking occurs between these two frequencies fR and fm (the ratio fR/fm is often an integer as in Fig. 2). Let us note at this point some similarities in this scenario with the one corresponding to fl and f2 : fR plays the role of fl and fm that of f2 : we think that, at these high rotation rates appears a flow with two boundary layers localized near the cylinders and a central region with an almost constant mean velocity. Fig. 2. Frequency components observed in the spectra P( f ) obtained for R/Re varying from 5 to 400. We can see the 0-dependence of the frequencies /g (a) and /R (A). The points (~, A, v) correspond respectively to the harmonics 6 fB, 7 fB, 8 fB, to the modulation mode fm and to the mode f,. 2.2 VARIATION OF THESE MODES WITH F, v AND d. To have a better understanding of t

Equilibrium magnetization of a spin glass : is mean-field theory valid ?

Abstract: Measurement of field cooled magnetization of a AgMn 10.6 % alloy as a function of temperature between 4.2 K and 50 K and magnetic field from 26 to 9 000 gauss is performed in order to link the low field and high field regimes of a spin glass. This can possibly help to define a phase diagram in the (H, T) plane as proposed by De Almeida and Thouless and Parisi and Toulouse. A closer investigation of the vicinity of Tg, above Tg, allows to compare the magnetization curves with the specific prediction of the mean-field model of Sherrington and Kirkpatrick. A qualitative good agreement is found.

Specific heat measurements of organic superconductivity in (TMTSF) 2ClO4

Abstract: The specific heat of the organic superconductor (TMTSF)2ClO 4 has been measured between 0.4 and 2 K. A large anomaly of the electronic contribution at 1.22 K has been attributed to the onset of three-dimensional superconducting order. There is a large magnetic field dependence of the electronic contribution above 1.22 K which is not characteristic of a normal conducting state. The application of a magnetic field of 63 kOe along the c*-axis of the single crystals restores a ground state exhibiting a very low density of states at the Fermi level (a narrow gap semiconducting or a semimetallic state). A phase transition towards a conducting state with a finite density of states at Fermi level is visible around 1.4 K. Our specific heat results support the existence of a wide 1-D superconducting fluctuating regime.

A new method of general use to obtain random powder spectra in 57Fe Mössbauer spectroscopy : the rotating-sample recording

Abstract: In the case of unpolarized 57Fe Mossbauer spectrometry, a method is described which provides the equivalent random powder spectrum for any sample, with any hyperfine interaction. The spectrum is recorded while the sample is rotated stepwise within a plane lying at 35.3° from the radiation direction. An alternative method consists in superimposing spectra for 4 orientations of the sample in the same plane.

Study of the deformation of ferrofluid droplets in a magnetic field

Abstract: We have studied the deformation of large magnetic agglomerates (2 to 20 μm) in a weak magnetic field (up to 10 gauss) for a new kind of ferrofluid The ellipsoid shape of the agglomerate is due to a competition between magnetic energy which favours elongated agglomerates in the field direction and surface energy which favours a spherical shape We can deduce a value of the interfacial tension of the agglomerates σ = (15 ± 02) 10-4 ergcm -2

Two-dimensional electronic properties of the purple potassium molybdenum bronze K0.9Mo6O17

Abstract: 2014 The electrical and magnetic properties between 2 K and 300 K, the low temperature specific heat and the crystal structure at 300 K have been studied on single crystals of K0.9Mo6O17 grown by the electrolytic reduction technique. K0.9Mo6O17 is found to be a quasi two-dimensional metal; this is consistent with the structural data. The transition which takes place below 120 K is due to the partial opening of a gap at the Fermi surface, possibly related to the onset of a charge density wave. J. Physique LETTRES 43 (1982) L-59 L-65 15 JANVIER 1982, Classification Physics Abstracts 72.15E 61.60 65.40E

Characteristics and energy balance of a plasma column sustained by a surface wave

Abstract: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Characteristics and energy balance of a plasma column sustained by a surface wave M. Chaker, P. Nghiem, E. Bloyet, Ph. Leprince, J. Marec

A new thermotropic smectic phase made of ribbons

Abstract: 2014 From microscopical observations and structural studies on the mesophases of a new thermotropic polar compound 2014 the nitrobenzoyloxybenzoate of octylphenyl 2014 we have shown the existence of a novel fluid mesophase built with ribbons forming a two-dimensional oblique lattice. We propose a crude model based upon structure factor calculations. J. Physique LETTRES 43 (1982) L-327 L-331 ler MAI 1982, Classification Physics Abstracts 61. 30E 64. 70E

EPR and electrical conductivity of the organic superconductor di-tetramethyltetraselenafulvalenium-perchlorate, (TMTSF)2ClO4 and a metastable magnetic state obtained by fast cooling

Abstract: EPR and electrical conductivity measurements under controlled thermal cycles demonstrate that a phase transition is occurring at about 22 K in (TMTSF)2ClO4. Slow cooling (12 K/h) yields a stable ground state exhibiting Pauli paramagnetism above and superconductivity below 1.2 K. In contrast, fast cooling (30 K/min.) yields a metastable magnetic (SDW) state below 4 K as indicated by increasing resistivity and disappearance of the EPR signal with decreasing temperature.

Magnetocaloric investigation of (H, T) phase diagram of CuMn spin glass

Abstract: 2014 The magnetocaloric effect has been used to determine the phase diagram (H, T) of a CuMn spin glass. Our results suggest the presence of two lines : the spin glass-paramagnetic boundary line Hc(T) and a crossover line Hm(T) separating a pure Curie paramagnet from a non-Curie paramagnet. The data obtained for the derivative (~M/~T)H obey a scaling law and give an estimation of the critical exponent 03B32 different from its « mean field » value. J. Physique LETTRES 43 (1982) L-153 L-158 Classification Physics Abstracts 75.30S 65.50 1 er MARS 1982, The nature of the transition from the paramagnetic to the ordered spin glass state remains one of the most interesting and exciting problems in solid state physics. For many years, theoreticians and experimentalists were faced with the same question : is the spin glass a new phase, to be distinguished from a paramagnet resulting from a thermodynamic phase transition, or trivially a metastable state : the result of a progressive freezing phenomenon ? Recent theoretical work [1] on the infinite range model shows the richness as well as the subtlety of the techniques needed to answer this question. The following new features are of physical interest : i) the breaking of linear response theory (at least for magnetic properties) in the spin glass phase; ii) the regular behaviour of linear response functions (first derivatives of free energy), with a singular behaviour of non-linear response functions (higher order derivatives, when the spin glass state is approached from the paramagnetic side); iii) the importance of the entropy S(T, H) as a key quantity in understanding the physics of spin glass. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:01982004305015300 L-154 JOURNAL DE PHYSIQUE LETTRES For a long time, attention was focused on the cusp at 7~ of the low-field a.c. susceptibility, considered as the signature of a true phase transition at this temperature. The variations of T~ with frequency, observed later in many spin glasses [2], was the first evidence, showing the weakness of the cusp argument. The presence of hysteresis and slow relaxation of remanent magnetization and of the associated energy [3] are now known to be characteristic properties of spin glasses below the temperature Tc of the susceptibility cusp. A considerable amount of work has been needed [4] to clarify the situation giving rise finally to the following set of « golden rules » : : 1) field cooling yields a quasi-equilibrium state (minor instabilities); 2) changing a magnetic field, by a small amount, at T Tc yields non-equilibrium and aftereffects (major instabilities) ; 3) for a given procedure of application of the field variations, the induced non-equilibrium state is a function of the reduced variable T In (t~~o), of associated time and temperature. Many illustrations of the validity of these golden rules have been given during the last few years [4]. In particular rule (1) gives the route towards the equilibrium state. Rules (2) and (3) indicate that any measurement obtained with a field variation must, because of its non-equili. brium character, be carefully considered. In this letter we report the results of magnetocaloric measurements on a CuMn spin glass in a large range of applied magnetic fields (0 H 5 kG), and temperatures (1 K T 10 K). The measurements were made on a 6.65 g, 0.25 at. %, polycrystalline sample of irregular shape. The temperature of the lac cusp is Tc = 3.53 K, and the Curie-Weiss temperature 6 obtained from very high temperature susceptibility measurements was 0 $ 0.1 K. The basis for the magnetocaloric effect is nothing other than the variation of the temperature of an adiabatically isolated substance with external magnetic field. This variation is related to the magnetization by where T is the temperature, H is the magnetic field, CH is the total specific heat of the sample in a magnetic field and M the magnetization of the sample. Bearing in mind the Maxwell relation it is easy to see that the magnetocaloric effect (aT/aH)s gives directly the isothermal variation of the entropy with a magnetic field, as well as the variation of magnetization with temperature at a fixed field. It is interesting to recall that this effect was, in the early days of the century [5], the first experimental evidence for spontaneous magnetization in a ferromagnet, as well as the first check of the mean field theory. Usually, the adiabatic variation of temperature vs. applied magnetic field is a sensitive probe to determine changes in the nature of spin ordering as a function of temperature and applied magnetic field [6]. This is exactly our purpose here. After a field cooling in a field Ho, starting from T ~> T c down to T ~ 1 K, we measure the magnetocaloric effect AT associated with small and slow variations AH around Ho (typically AHIHO 0.5 % at 10 %, this variation being established within 5s). The calorimetric measurements were made using apparatus and techniques to be described elsewhere [7]. The sensivity of the temperature measurement was better than 106 K. Heating by eddy currents was eliminated in these measurements by taking into account the proportionality of this effect with OH 2, in contrast to the measured magnetocaloric effect AT which has the same sign as AH. L-155 MAGNETOCALORIC INVESTIGATION OF CuMn Figure 1 shows the variation of the magnetocaloric effect AT in our sample against temperature at different fields (AH = 25 G). Using equation (1) and specific heat data, we can deduce for each Ho the temperature variation of the derivative (~M/~T)~, (the relative variation of the specific heat due to the magnetic field Ho is less than 2 x 103 [8] in the range of interest). In figure 2 we show (~M/~T)~ scaled by the cooling field Ho. The weakness of AH seems to allow the use of equation (1) below Tc, all the more as the magnetocaloric effect remains reversible in our experiment. However the verification of the Maxwell relation in the spin glass state must be carried out in the future. ’ Fig. 1. Magnetocaloric effect at different values of Ho. The arrow shows the position of 7~ = 3.53 K. Fig. 2. (~M/~T)~.~o’ ~ deduced from equation (1) and experimental results of figure 1. L-156 JOURNAL DE PHYSIQUE LETTRES Starting from high temperature, we obtain a Curie regime (C = 9.21 x 105 K . emu/g . G) followed by a minimum of (-~-) showing a departure from a Curie regime and finally the B~/~o spin glass region with vanishing values. The variation (aM/a T)Ha . Ho ’ vs. T near Tc becomes sharper in vanishing fields Ho, which suggests a possible abrupt discontinuity at (Ho ~ 0, T ~ T~). For each value of Ho we find two characteristic temperatures : 1) Tm > T, giving the position of the minimum of (~M/~r)~(i.e. inflexion point of magnetization M(T) at Ho) ; 2) Tc(Ho) Tc defined by the point where the tangent at the inflexion point of (aM/aT)Ho intersects the temperature axis. These characteristic values for each Ho are plotted in the diagram (H, T) shown in figure 3. The two lines Hm(T) and Hc(T) start from (T = 7~, H = 0) and divide the diagram into three regions : a spin glass phase (H ~ 0, T ~ 0), a Curie paramagnet (T ~> Tc, H ~ 0) and a nonCurie paramagnet in the intermediate region (see below). The line Hm(T ) is a crossover line, dividing the paramagnetic phase into two regions. The first of these is a Curie one, where the magnetization is a function of HIT only. In our case M ~ CHIT, because 0 ~ 0 K. In the second region, the magnetization is expected to have a more complicated expression. For instance, at T > Tc and H ~ 0 we suspect the following [9-11] behaviour : where X denotes the Curie susceptibility (linear susceptibility) and a(T) is a singular correction : a(T) ~ (T T~)~y2 (non-linear susceptibility), which measures the rigidity of the condensed state. Hm(T) is the field value where the singular correction becomes as important as the leading term (in « mean field » theory, y2 = 1). Fig. 3. Phase diagram (H, T) determined from magnetocaloric effect. Full line H c( T) is the boundary line spin glass-non-Curie paramagnet, and dashed line Hm(T) is the crossover line Curie-non-Curie paramagnet. L-157 MAGNETOCALORIC INVESTIGATION OF CuMn More generally, M(T, H) is the sum of two contributions : a regular contribution M~(7B H) and a singular contribution Msing(T, H), obeying the universal scaling law [10] where P is the exponent of the order parameter q. A previous determination ofj8 [12] gives ~ ~ 1, close to the « mean field >> value. We deduce from (4) : Taking into account the first order term in F(x), we deduce two points from the preceding equation : the temperature of the minimum of (aM/aT)Ho (i.e. (02 MIDT 2)H. = 0) depends on the field cooling by the following relation : the amplitude of (aMs;ng/aT ) at this minimum is related to Tm through : From these two relations and our experimental results at T = T.(HO), we determine the critical exponent 3.3 Y2 4. Admitting (4) as the scaling law and assuming p =1 [12], we obtain, with all our results for T > Tc, the best fit of (aMs;ngiaT ) Ho 1 for Y2 = 3.5 instead of y~ = 1 as in the « mean field » theory (Fig. 4). This universal behaviour supports our assumption /3 ~ 1. The line Hc(T) is identified as the boundary line of the spin glass phase. Hc(T) increases rapidly as T decreases from 7~. This critical line varies as predicted by the « mean field » theory in low fields. Fig. 4. Universal plot of (~M~/~T)~.Ho~ 1 as function of ~(T7~)’~~ from data obtained at T > T~. L-158 JOURNAL DE PHYSIQUE LETTRES The strong variation of Hc(T) at lower temperatures converges asymptotically towards the behaviour predicted by the « mean field » theory [13] : More details will be published elsewhere. To conclude, the magnetocaloric effect was used for the first time to investigate the (H, T) phase diagram of a CuMn spin glass. We have shown the existenc

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Random antiphase state and frustration in two dimensions

Abstract: 2014 The phase diagram of the frustration model of random interactions ± J between nearest neighbour Ising spins on a square lattice is studied in the (T, x) plane : T temperature, x concentration of antiferromagnetic interactions. At T = 0 K exact ground states are generated by a new algorithm of graph theory and maps of rigid bonds or solidary spins for all ground states are obtained. At intermediate x it is found a new phase made up of erratic magnetic walls (lines). At T ~ 0 K a simple renormalization group approach confirms the existence of the random antiphase state. J. Physique LETTRES 43 (1982) L-347 L-354 15 mm 1982, Classification Physics Abstracts 75.10H It is currently admitted that, in two dimensions, the standard model of Ising spin glasses based on a symmetrical distribution of random interaction J, p(J) = p(J), does not exhibit any spin glass phase but only paramagnetism at T ~ 0 K. By varying the concentration x of negative interactions (from x = 0.5 to x = 0), a phase diagram (x, T) is explored and the previous attempts [1] concluded to the existence of a transition from paramagnetism to ferromagnetism at low concentration x and nothing else. Using a new algorithm for generating exact ground states we have found a new phase nested near the ferromagnetism region that we have called « random antiphase state » (RAS). 1. Frustration and the Chinese postman’s problem The Hamiltonian which has been studied here is written : where ~;, 7j = ± 1 are Ising spins on square lattice of size L x L = N and J;~ the random interaction between nearest neighbour spins, with the probability x for Jij = J and 1 x for Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019820043010034700 L-348 JOURNAL DE PHYSIQUE LETTRES Jij = + J. The construction of ground states for a given sample and interactions is a complicated problem which cannot be solved by a Monte Carlo method [2]. It turns out that the relaxation process traps the system into low energy metastable states of very long lifetime [3]. Only special procedures such as the matching method (by hand [4] or computational [5]) or exact calculation [6] of partition function can give information at low or zero temperature. Here a new algorithm is proposed which is not only able to generate one ground state for each sample but some invariant properties for all the ground states. The starting point is the exact correspondence between the frustration model and the Chinese postman’s problem [7, 8], which is defined in the following way : a postman delivers mail along a set (graph G) of streets (edges) connecting cross-roads (nodes). What is the minimum round from the post office ? For even nodes only the solution is simply given by a Eulerian path but when odd nodes are present the postman walk is constrainted by repeated crossings between odd nodes. Let us now recall the basic rules [9] of the frustration problem : the frustrated plaquettes are defined by an odd number of negative bonds on the perimeter. They are sources or sinks for a set of violated bonds called strings : a ground state energy is obtained when the total length of strings is minimum. It can be shown [10] that both rule sets are equivalent according to the dictionary : odd nodes +-+ frustrated plaquettes repeated streets +-+ violated bonds round length +-+ frustration energy . The polynomial algorithm of Edmonds which solves the Chinese postman’s problem has been used here for generating ground states of frustration model. It is described in details elsewhere [10] and only summarized here : (i) A primal problem is defined where a bond variable xij has value 0 or 1 for normal or violated bonds. Odd subsets S of frustrated plaquettes are delimited by frustrated contours. The integrality condition for xij is relaxed by adding linear constraints on these contours. (ii) The dual problem associated to (i) is stated in terms of dual variables ys related to frustrated contours. By analogy with dislocation theory ys may be understood in terms of « line tension » of a frustrated contour analogous to « Volterra » circuit surrounding dislocation cores (frustrated plaquettes). (iii) Using the weak theorem of complementary slackness [11] a simple criterion for optimality of primal and dual solutions is settled (iv) The spin configuration is progressively improved by flipping spin clusters having any irregular form. In contrast to Monte Carlo technique it is a non local algorithm which can overcome metastability. (v) Two types of boundary conditions can be chosen by the algorithm for optimality : periodic or antiperiodic where the corresponding spins of opposite sides are parallel or antiparallel. This additional degree of freedom plays a crucial role in the description of the magnetic properties of ground states. The rigidity of bonds is studied by a post-optimal algorithm. A rigid bond is by definition [10, 13] a violated bond (or non violated) for all the ground states. A simple procedure is used to obtain the map of rigid bonds : starting from a ground state a violated bond is rigid if, for any E > 0 added to its weight I Jij the optimality of the solution is not destroyed (similar procedure is possible for unviolated bonds). Hence, despite the exponential degeneracy for ground states [6], this algorithm has only 0(N 2) complexity [12] where N denotes the total number of spins. All the details of the numerical experimentation are reported in reference [10]. Let us just recall a few indications : the size is ranging from 10 x 10 up to 20 x 20, the concentration x between 0 L-349 RANDOM ANTIPHASE STATE AND FRUSTRATION and 0.5 and the number of samples : 248. Twp types of defects have been found from the analysis of the morphology of these ground states. The fracture lines or contours of zero energy running from one side to another which proliferate at x > 0.15. These defects, which have been conjectured previously [5, 14] appear as alternating cycles of an equal number of violated and non violated bonds in such a way that the energy is invariant under a change of the matching. The fracture line creeps along the corridor between the clusters of rigid bonds. It indicates a destruction of the macroscopic rigidity and implies that the magnetic long-range correlation cannot persist above x > 0.15. Actually, in this region only small finite rigid clusters persist and the percolating rigid cluster is destroyed by fracture lines. In conclusion, here the ground states are disordered and the phase looks like superparamagnetism. Fig. 1. Random Antiphase State. The black and white circles represent the Ising up and down spins in a rigid configuration (same orientation for all the ground states). The loose spins the orientation of which change from one ground state to another are not marked. The magnetic wall separates two domains of up and down spins. Periodic boundary conditions are applied on the vertical edges while antiperiodic conditions work on the horizontal edges. The magnetic walls appear when the samples are rigid, therefore below x = 0.15, and are revealed by the fact that our algorithm chooses in almost all cases the antiperiodic boundary conditions. The frequency of occurrence of each type of defects increases abruptly at different values of x : around x ^_r 0.10 for the magnetic walls and x ~ 0.15 for the fracture lines. A magnetic wall is illustrated in figure 1 : it crosses the rigid bonds as well as living bonds. It is constituted by an unequal number of non violated negative bonds and violated positive bonds, in such a way that any alternation of the matching results in an increase of the energy. Since this defect exists in the range of rigidity, the magnetic correlation of the spins in the rigid cluster is equal to one although the total magnetization vanishes. It is therefore a highly correlated state, named Random Antiphase State, where the spin correlation function of the type S(0) S(R) ~o (averaged over all the ground states) has its maximum value inside the percolating cluster of rigid bonds. L-350 JOURNAL DE PHYSIQUE LETTRES 2. Real space renormalization approach. The renormalization in real space is a very simple method for the determination of a phase diagram by identifying the nature of the phase for each value of T and x. Consider two spins connected through a cluster of spins with { J;~ } or { t;~ = tanh (J;~/T) ~ a given configuration of the interactions. By summing over the spin states of the cluster (partial trace) an effective interaction is built t’(1 tij }) between the two spins. The iteration relation leads to a fixed value which identifies the nature of the phase, for instance t’ = 0 for the paramagnetic phase or t’ = 1 for the ferromagnetic state. For disordered systems the iteration procedure is applied on the probability distribution p(t) rather than t. The integral equation for the «fixed » probability density is very complicated and no analytic solutions can be found. For square lattice a class of special clusters having the self dual symmetry turned out to be very efficient for the problem of conduction in random resistors [15] as well as dilution disorder problem [16]. The algebraic duality for the t’s (Kramers-Wannier) has a geometrical correspondence by the rule of construction of dual bonds intersecting the primal interactions. The self-dual clusters are the special class of clusters of spins which reproduce themselves by this simple rule. Beyond the trivial cluster of one bond, one finds the H-cluster or Wheatstone bridge in two dimensions (b = 2) which possesses this property. The next cluster (b = 3) in 2 dimensions contains 13 bonds. , Let t = tanh 2013 be the critical value corresponding to the critical temperature T e for x = 0. ~ e For each starting value t the iteration relation leads to the fixed point of the paramagnetic phase t = 0 for instance while the dual relation leads to the other fixed point, the ferromag