Showing papers in "European Physical Journal B in 1981"

On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state

Abstract: It is pointed out that chemical reactions which show an absorbing stationary state in the master-equation approach (e.g. Schlogl's first reaction) exhibit nevertheless a second order phase transition in non-zero dimensional macroscopic systems. The relation to Reggeon field theory is given more directly than by Grassberger et al. using the functional integral formalism of statistical dynamics. As a new result the correlation length exponent ν and the order parameter exponent β are found toO(e2) in an ɛ-expansion around the upper critical dimensiondc=4.

Bounds on the density of states in disordered systems

Abstract: For a class of tight-binding models governed by short-range one-particle Hamiltonians with site-diagonal and/or off-diagonal disorder and continuous distribution of the matrix elements it is proven that the averaged density of states does neither vanish nor diverge inside the band. This refutes for these models conjectures that the density of states vanishes or diverges at the mobility edge.

Anomaly in the band centre of the one-dimensional Anderson model

Abstract: We calculate the density of states and various characteristic lengths of the one-dimensional Anderson model in the limit of weak disorder. All these quantities show anomalous fluctuations near the band centre. This has already been observed for the density of states in a different model by Gorkov and Dorokhov, and is in close agreement with a Monte-Carlo calculation for the localization length by Czycholl, Kramer and Mac-Kinnon.

Finite size scaling analysis of ising model block distribution functions

Abstract: The distribution functionP L (s) of the local order parameters in finite blocks of linear dimensionL is studied for Ising lattices of dimensionalityd=2, 3 and 4. Apart from the case where the block is a subsystem of an infinite lattice, also the distribution in finite systems with free [P (s)] and periodic [P ] boundary conditions is treated. Above the critical pointT c , these distributions tend for largeL towards the same gaussian distribution centered around zero block magnetization, while belowT c these distributions tend towards two gaussians centered at ±M, whereM is the spontaneous magnetization appearing in the infinite systems. However, belowT c the wings of the distribution at small |s| are distinctly nongaussian, reflecting two-phase coexistence. Hence the distribution functions can be used to obtain the interface tension between ordered phases. At criticality, the distribution functions tend for largeL towards scaled universal forms, though dependent on the boundary conditions. These scaling functions are estimated from Monte Carlo simulations. For subsystem-blocks, good agreement with previous renormalization group work of Bruce is obtained. As an application, it is shown that Monte Carlo studies of critical phenomena can be improved in several ways using these distribution functions:(i) standard estimates of order parameter, susceptibility, interface tension are improved(ii) T c can be estimated independent of critical exponent estimates(iii) A Monte Carlo “renormalization group” similar to Nightingale's phenomenological renormalization is proposed, which yields fairly accurate exponent estimates with rather moderate effort(iv) Information on coarse-grained hamiltonians can be gained, which is particularly interesting if the method is extended to more general Hamiltonians.

Field-theoretical approach to static critical phenomena in semi-infinite systems

Abstract: The critical behaviour of a semi-infinite system withO(n) spin symmetry is studied in 4-ɛ dimensions near the ordinary transition using renormalization-group methods of field theory and ɛ-expansion techniques. It is found that, to all orders in ɛ, all surface exponents can be expressed in terms of two bulk exponents and a single surface exponent which follows from the anomalous dimension of the derivative ∂⊥ φ(x ∥,0) of The order parameter ϕ(x‖,x ⊥) at the surface (x ⊥=0). As a byproduct, Barber's scaling law 2γ1 − γ11 = γ + ν is obtained. The surface exponents are calculated to second order in ɛ. Our results show that the scaling relationη ∥ = ν−1 proposed by Bray and Moore is incorrect. The behaviour of various scaling functions close to the surface (i.e. forx ⊥ ≪correlation length) is determined with the help of short-distance expansions. We also treat corrections to scaling and logarithmic corrections in four dimensions. Our results for the logarithmic corrections of the layer and local susceptibilities disagree with those obtained by Guttmann and Reeve.

Phase diagram for three-dimensional correlated site-bond percolation

Abstract: The Coniglio-Stanley-Klein model is a random bond percolation process between the occupied sites of a lattice gas in thermal equilibrium. Our Monte Carlo simulation for 403 and 603 simple cubic lattices determines at which bond thresholdp Bc , as a function of temperatureT and concentrationx of occupied sites, an infinite network of active bonds connects occupied sites. The curvesp Bc (x, T) depend only slightly onT whereas they cross over if plotted as a function of the field conjugate tox. Except close toT c we find 1/p Bc to be approximated well by a linear function ofx, in the whole interval between the thresholdx c (T) of interacting site percolation atp Bc =1 and the random bond percolation limitx=1 atp Bc =0.248±0.001. Thisx c (T) varied between 0.22 forT=0.96 (coexistence curve) and 0.3117±0.0003 forT=∞ (random site percolation). At the critical point (T=T andx=1/2) we confirmed quite accurately the predictionp Bc =1-exp(−2J/k B T c ) of Coniglio and Klein. As a byproduct we found 0.89±0.01 for the critical exponent of the correlation length in random percolation.

Modulated phase of an ising system with competing interactions on a Cayley tree

Abstract: A system with competing nearest-neighbour and next-nearest-neighbour interactions is considered on a Cayley tree The phase diagram contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature The variation of the wavevector with temperature in the modulated phase is studied in detail, it shows narrow commensurate steps between incommensurate regions (“incomplete devil's staircase”) The behaviour of the coherence length near the different transitions is also analyzed

Self-avoiding-walks (SAW's) on diluted lattices, a Monte Carlo analysis

Abstract: A Monte Carlo study of SAW's on a diluted diamond lattice is presented. We find that the exponentv does not change by dilution,v≈0.59 as in the undiluted case, in contrast to the original conclusion of Chakrabarti and Kertesz. This result cannot be understood by the Harris criterion. At the percolation concentrationp c of the lattice we find a higher exponentv pc ≈2/3. A scaling form of the crossover between these exponents nearp c is proposed and found to be consistent with the Monte Carlo results.

Monte Carlo study of entropy for face-centered cubic Ising antiferromagnets

Abstract: A face-centered cubic Ising model with nearest neighbor antiferromagnetic exchangeJ nn in the presence of a magnetic fieldH is investigated by Monte Carlo methods. Free energy and entropy of the model are obtained by integrating the equation of state along various paths, starting at suitable reference states. It is shown that at low temperatures first-order phase transitions can be located with very good precision. At the two critical fieldsH c1/|J nn |=4,H c2/|J nn |=12 a residual ground-state entropyS(0) is found, which is estimated as aboutS(0)/k B ≈(ln 2)/3 in both cases. In the presence of a ferromagnetic next-nearest neighbor exchange there is no longer a nonzero entropy at the critical fields, however. ForR+J nnn /J nn +−1 we find the same structure of the phase diagram as qualitatively predicted by Domany et al., where lines of 3-state and 4-state Potts model-like transitions meet at a multicritical point atH=0. Some consequences of our results for interpreting the ordering of face-centered cubic binary alloys are also discussed.

Calculation of spin correlations in two-dimensional Ising systems from one-dimensional kinetic models

Abstract: Kinetic spin models of the type first introduced by Glauber are considered with the most general choice of transition rates. It is shown that their time evolution operator can be related to the transfer matrices of certain two-dimensional Ising lattices. This allows an exact calculation of spin correlation functions at certain temperatures. Specifically we show that for the triangular antiferromagnet this special temperature corresponds to the disorder point. For the Hamiltonian version of the ANNNI model the corresponding result restricts in an important way the possible structure of the phase diagram.

s-Polarized nonlinear surface polaritons

Abstract: An exact solution of Maxwell's equations is found, corresponding to ans-polarized nonlinear surface polarition, at the planar interface between two dielectric media, one of which is optically unaxial and is characterized by a diagonal dielectric tensor whose elements depend on the amplitude of the electric field according to e11=e22=e0(ω)+a(ω) (|E1|2+|E2|2), e33=e(ω). Such modes have no counterpart in the corresponding linear system.

On phase transitions in Schlögl's second model

Abstract: We study Schlogl's second model, characterized by chemical reactions $$\begin{array}{*{20}c} {2X\underset{{k_2 }}{\overset{{k_1 }}{\longleftrightarrow}}3X,} & {X\underset{{k_4 }}{\overset{{k_3 }}{\longleftrightarrow}}0,} \\ \end{array} $$ ind-dimensional space. The reactions are assumed to be local; local fluctuations are fully taken into account, and particle transport occurs via diffusion. In contrast to previous investigations, we find no phase transition whenk 4≠0 andd<4. Fork 4=0,k 3≠0, and 1≦d<4, we find a second-order phase transition which is in the same universality class as the transition in Schlogl's first model. Only ford≧4 we do find the first-order transition found also by previous authors. These claims are supported by extensive Monte Carlo calculations for various realizations of this process on discrete space-time lattices.

Grüneisen parameter of cerium compounds with unstable 4f shells

Abstract: We give experimental results of magnetic susceptibility, thermal expansion and elastic constant measurements for CeSn3 and CePd3. We interpret these results with a phenomenological scaling function for the free energy and we include a brief discussion of CeAl3. The coupling between the electronic system and the lattice can be described by an electronic Gruneisen parameter Ωg associated with the unstable 4f system which turns out to become a system specific constant far below the fluctuation temperatureT0. The coupling parameter T0Ωg is an order of magnitude larger than the coupling constant for stable valentRE systems extracted from crystal field effects. A generalization to include magnetic field dependent effects is also given.

Conductivity and localization of electron states in one dimensional disordered systems: Further numerical results

Abstract: The localization of the electron states and dc-conductivity of the one dimensional Anderson model are investigated with various numerical procedures. It is found that the eigenstates are always exponentially localized and that in the center of the band the localization length is proportional to the inverse square of the disorder. The dc-conductivity, as obtained by using the Kubo-Greenwood formula, obeys the central limit theorem for any finite imaginary frequency, with a variance, which is inversely proportional to the squareroot of the number of states contributing to the transport. There is no exponential length dependence of the Kubo-Greenwood conductivity within this model. The conductivity tends to zero only in the limit of vanishing imaginary frequency.

The magnetic behavior of CeB6: Comparison between elastic and inelastic neutron scattering, initial susceptibility and high-field magnetization

Abstract: We report measurements of the elastic and inelastic neutron scattering, initial susceptibility and high-field magnetization on thoroughly prepared poly- and single crystalline samples of CeB6. Part of these experiments have been performed at temperatures down to 60 mK and magnetic fields up to 70 kOe. Our neutron-diffraction data provide the first proof that CeB6 is an antiferromagnet belowTN≃2K as has been suggested by previous bulk experiments. The reduced value of the low-temperature magnetic moment both below and aboveTN points to the existence of a Kondo effect of theΓ7 crystal-field (CF) ground state of Ce3+. From the low-temperature width of the quasielastic neutron line, the Kondo temperature is inferred to beTK≃3 K. The thermal variation of the initial susceptibility (forT>20K) is semiquantitatively explained invoking, besides the Kondo effect, aΓ7-Γ8 CF splitting of ≃70 K and magnetic interactions, which are about 10 times stronger betweenΓ8 states than those betweenΓ7 states. This largeΓ8-Γ8 exchange interaction is also assumed to account for the most striking result of this work, i.e. the lack of any CF-transition peak up to 44 meV in our inelastic neutron-scattering spectra.

Observation of the neutron magnetic resonance energy shift

Abstract: Using a high resolution backscattering instrument the energy shift caused by the Zeeman splitting and the inelasticity of the interaction of neutrons with a neutron magnetic resonance system could be observed. Various applications concerning the realization of a dynamical neutron polarization system, the pumping of neutrons into a certain energy interval and the production and handling of ultra cold neutrons are discussed.

Nonequilibrium properties of electron-hole plasma in direct-gap semiconductors

Abstract: The gain spectra of the electron-hole plasma recombination in CdS are investigated as a function of the excitation conditions and of the lattice temperature. From a lineshape analysis which includes such many-body effects as collision broadening, single-particle energy renormalization and excitonic enhancement, average plasma parameters are obtained. In contrast to the predictions of quasi-equilibrium theory, one finds that the electron-hole plasma does not reach a full thermal quasi-equilibrium in direct-gap materials because of the short lifetimes of the carriers. The nonequilibrium effects are shown to lead to the formation of electron-hole plasma density fluctuations. No well-defined coexistence region exists. The experimental results in the phase transition region can consistently be explained by theoretical treatments of this nonequilibrium phase transition.

Finite-size behaviour of the two-dimensional ANNNI model

Abstract: The two-dimensional axial next-nearest neighbour Ising (ANNNI) model of finite size with periodic boundary conditions is studied by the Monte Carlo method. The model shows an interesting finite size dependence in connection with its oscillatory correlations pretending for finite systems a Lifshitz point in one part of the phase diagram, while the infinite system appears to display one in another part of the phase diagram.

Theory of inelastic atom-surface scattering: Examples of energy distributions

Abstract: The theory of the energy distribution of atoms scattered inelastically by solid surfaces which was developed previously is applied to various examples. The dependence of the results on a number of parameters is studied in detail. The importance of many phonon contributions as compared to the validity of first order distorted wave Born approximation is considered in particular. It turns out that low energy He atoms scattered by heavy transition metals provide a good example for which one phonon emission (or absorption) dominates. All other noble gases show appreciable many phonon contributions increasing, of course, with increasing mass of the noble gas and temperature of the solid. For heavy noble gases such as Kr and Xe the energy distribution approaches a gaussian, the width of which is due to the thermal and zero-point motion of the lattice. This width is quite large and thus probably masks most of the ‘fine structure’ of the energy distribution occuring in classical trajectory calculations. We have also tried to apply the theory to light diatomic molecules. Although the results are less certain, partly because of the neglect of the internal motion of the molecules and partly because of uncertainties in the interaction parameters, one probably can expect appreciable many phonon effects already for H2 and, of course, more so for N2 and O2. Recent experimental results on the Debye-Waller factor of Ne/Cu can be reproduced with reasonable potential parameters.

Self-consistent current relaxation theory for the electron localization problem

Abstract: The self-consistent current relaxation theory for the Anderson transition is generalized to include quantum interference effects. The influence of long-ranged potential fluctuations as opposed to short-ranged ones is discussed and for dimensionalityd>2 a crossover for the dynamical conductivity from a regime with Wegner scaling to one with the scaling laws for classical percolation is found. Ford=2 an abrupt transition from strong to extremely weak localization is obtained.

Theory of the upper critical fieldH c2 in antiferromagnetic superconductors

Abstract: The influence of antiferromagnetic order on the upper critical field of superconductors is investigated within the framework of Eliashberg theory. Below the Neel temperature the superconductor is characterized by Cooper pairs of quasiparticle states which are related by time reversal followed by a lattice translation. This leads to a change in the effective attraction between the quasiparticles which we calculate explicitely for the Chevrel phase compounds RE Mo6S8 (RE=Gd, Tb, and Dy). The results for the upper critical fields clearly show that our theory yields a consistent explanation of the experimentally observed anomalous behaviour.

Electrical and thermal conductivity of CePd3, YPd3, GdPd3 and some dilute alloys of CePd3 with Y and Gd

Abstract: Resistivity and thermal conductivity of the intermediate valence compound CePd3 between 1.3 and 300 K are compared with those of the nonmagnetic and magnetic reference compounds YPd3 and GdPd3 and of alloys of the type Ce1−xRE x Pd3 with RE=Y, Gd and 0.01

Thermal expansion and specific heat of intermediate valent YbCuAl

Abstract: The specific heat, thermal expansion and resistivity was measured for the intermediate valence compound YbCuAl and its reference compound LuCuAl between 1.5 and 400 K. All quantities show strong anomalies. The entropy of the specific heat anomaly is found to be nearR·ln9, the value expected for the entropy of a high temperature mixture of Yb-ions in the ratio dictated by the degeneracies of the Hund's rule groundstates of 4f 14 and 4f 13. TheT 3 coefficient of the low temperature specific heat of YbCuAl contains a large electronic contribution. The integrated thermal expansion anomaly indicates a shift of the valence by at least 3.5% towards 3+ between 1.5 and 310 K.

Random layered frustration models

Abstract: We study inhomogeneous two-dimensional Ising models with a random distribution of ferro- and antiferromagnetic couplings,Kij=±K, or equivalently a random distribution of frustrations. In particular, we considerRandom Layered Frustration models (RLF) where randomness is confined to the vertical direction. These RLF-models are solved exactly, i.e., partition function and free energy are obtained in closed form for an arbitrary random distribution of finite period. The phase transition is of Ising type. A simple formula for the transition temperature is derived which depends only on the mean coupling\(\overline {K_{ij} } \), but not on other details of the distribution. Both cases,Tc=0 andTc≠0, are possible. Groundstate energy and groundstate degeneracy, or equivalently the rest entropy, are determined. It is found that both the occurence or absence of a phase transition may be accompanied with vanishing or nonvanishing rest entropy. We also show that for the RLF-models a phase transition is excluded when all groundstates are connected with one another by local transformations which presumably holds generally. A remarkable result is that the transition of the ferromagnetic Ising model can be destroyed completely if one replaces an arbitrarily small fraction of ferromagnetic couplings by antiferromagnetic ones in a suitable way.

Monte Carlo renormalization of hard sphere polymer chains in two to five dimensions

Abstract: A renormalization group for polymer chains with hard-core interaction is considered, where a chain ofN0 links of lengthl0 and hard-core diameterh0 is mapped onto a chain ofN1=N0/s links of lengthl1 and hard-core diameterh1. The lengthl1 is defined in terms of suitable interior distances of the original chain, andh1 is found from the condition that the end-to-end distance is left invariant. This renormalization group procedure is carried through by various Monte-Carlo methods (simple sampling is found advantageous for short enough chains or high dimensionalities, while dynamic methods involving “kinkjumps” or “reptation” are used else). Particular attention is paid to investigate systematic errors of the method by checking the dependence of the results on bothN0 ands. It is found that for dimensionalitiesd=2, 3 only the nontrivial fixed-point is stable, where upon iteration the ratio δk=hk/lk tends to nonzero fixed-point value δ*, while ford=4,5 the method converges to the gaussian fixed point with δ*=0. Taking both statistical and systematic errors into account, we estimate the exponentv asv=0.74±0.01 (d=2) andv =0.59±0.01 (d=3). The results are consistent with the expected crossover exponents ϕ =1/2 (d=3) and ϕ=1 (d=2), respectively.

Generalized Ginzburg-Landau equations, slaving principle and center manifold theorem

Abstract: The Generalized Ginzburg-Landau equations, introduced by one of us (H.H.), are considered in a simplified version to clarify their relation to the center manifold theorem.

The statistics of self-avoiding walks on a disordered lattice

Abstract: The relevance of lattice disorder on the “critical behaviour” of self-avoiding walks is discussed. A crossover from nonclassical to classical behaviour seems to take place.

Transport properties of intermediate valence compounds studied within the alloy analog approximation of the Periodic Anderson Model

Abstract: We use the Periodic Anderson Model (PAM) to describe the transport properties of intermediate valence compounds. The transport quantities of interest are related to the current-current response function. Therefore, a current operator being consistent with the PAM Hamiltonian must be defined. This aim is achieved by defining a proper particle density operator and using the continuity equation. The PAM is treated within the alloy analog approximation, i.e. it is replaced by the sum of two effective single-particle “alloy”-Hamiltonians, which are treated within the coherent potential approximation (CPA). Then the CPA for transport quantities is used to calculate the current-current response function. It is shown that for all reasonable assumptions for the conduction band and the hybridization dispersion the current vertex corrections vanish within the CPA. For different assumptions concerning the hybridization dispersion, we present numerical results for the temperature and parameter dependence of some transport quantities, in particular the static resistivity. The relevance of these results for the understanding of the typical experimental resistivity behaviour obtained for different intermediate valence compounds and possible shortcomings of our approach are discussed.

Solitons and magnons in Sine-Gordon like magnetic chains

Abstract: We present theoretical results on the dynamic structure factors of both the classical Sine-Gordon chain and thexy-like ferromagnetic chain in a symmetry breaking magnetic field. We investigate the lowest order corrections to the noninteracting soliton/magnon picture and show that interference effects between solitons and magnons considerably reduce the intensity of the soliton induced central peak. We discuss the additional contribution of two magnon processes to the central peak and find that the combined strength is in agreement with numerical results. We calculate magnon intensities including quantum effects and find that the intensity depends strongly on temperature and wavevector. Quantitative results are given for the one-dimensional magnet CsNiF3 and compared to neutron scattering data. The soliton induced line-width of the long wavelength magnon is also given.

Crystal field parameters and crystal field linewidths in the (REY)Pd3 and (REY)Al2 alloys

Abstract: The LLW-parametersx andW of dilute rare earth impurities (RE=Pr, Nd, Tb, Dy, Ho, Er, Tm;c≈0.05), in the cubic matrices YPd3 and YAl2 could be determined unequivocally in the crystal field scheme of Lea, Leask and Wolf by inelastic neutron scattering. The crystal field parameters derived fromx andW are not consistent with the point charge model. The ratio of N(EF)Jex for the (REY)Pd3 and (REY)Al2 extracted from the RE-linewidths correlates with the corresponding ratio extracted from their magnetic ordering temperatures.