Showing papers on "Phase transition published in 1982"
TL;DR: In this paper, the critical exponent γ in the relation between the dielectric constant and temperature (1/e − 1/em = C'-1x (T −Tm)γ) has been determined precisely for relaxor ferroelectrlics Pb(Mg1/3Nb2/3)O3, and a related solid solution 0.88Pb (Zn 1/3 Nb 2/3)-O3-0. I2PbT103.
Abstract: The critical exponent γ in the relation between the dielectric constant and temperature (1/e—1/em = C'-1x (T—Tm)γ) has been determined precisely for relaxor ferroelectrlics Pb(Mg1/3Nb2/3)O3, Pb(Zn1/3 Nb2/3)O3 and a related solid solution 0.88Pb (Zn1/3 Nb2/3)O3-0. I2PbT103, as well as for normal ferroelectrics BaTiO3 and K(Ta0. 55Nb0.45)O3. A high correlation of the γ value with the plase transition diffuseness has been found empirically. Moreover, this γ value is very close to another critical exponent γ* which is defined in the relation between the dielectric constant and hydrostatic pressure (1/e—1/em = C* (p—pm)γ*)
1,102 citations
TL;DR: In this article, the dielectric, piezoelectric and elastic properties of 0.91(PbZn1/3Nb2/3)O3−0.09PbTiO3 single crystals have been investigated as functions of temperature and applied electric field.
Abstract: The dielectric, piezoelectric and elastic properties of 0.91(PbZn1/3Nb2/3)O3–0.09PbTiO3 single crystals have been investigated as functions of temperature and applied electric field. Two multiple phase transitions at 68°C and 178°C, the crystal changing from the rhombohedral ferroelectric phase to tetragonal ferroelectric and then to cubic paraelectric, have been observed. Both the transitions are of first-order, but both are slightly diffused. Significant increases in the dielectric, piezoelectric and elastic constants are observed at the lower transition point. In particular, the sample poled along the pseudo-cubic [001] axis reveals anomalously large piezoelectric and electro-mechanical coupling constants at room temperature in the rhombohedral phase (d[001]//=1500×10-12 C/N, k[001]//=0.92).
900 citations
01 Jan 1982
TL;DR: For the critical exponents near the sol-gel phase transition, classical theories like those of Flory and Stockmayer predict one set of exponents, whereas scaling theories based on lattice percolation predict different exponents as discussed by the authors.
Abstract: For the critical exponents near the sol-gel phase transition, classical theories like those of Flory and Stockmayer predict one set of exponents, whereas scaling theories based on lattice percolation predict different exponents. The two groups of theories differ in their treatment of intramolecular loops, space dimensionality and excluded volume effects. In this article, the differences and similarities between the results of the competing theories are reviewed. For example, a gel fraction like (p-pc)β vanishes for conversion factors p very close to the gel point pc, the weight average molecular weight diverges as (pc-p)−γ for p very slightly below pc, and the radius of macromolecules at the gel point p=pc varies as the ϱ-th power of the number of monomers in that macromolecule. Classical theories predict β=γ=1 and ϱ=1/4 whereas the percolation theory gives β ≃ 0.45, γ ≃ 1.74 and ϱ ≃ 0.40. We also generalize the percolation concept to include interaction effects and concentration fluctuations; in this case the sol-gel phase transition may be connected with a phase separation.
695 citations
TL;DR: In this paper, the universe might have had a prolonged exponentially expanding phase caused by its being stuck in a metastable state of the grand unified phase transition, and the only way that it could exit from this exponential expansion without introducing too much inhomogeneity or spatial curvature would be through a homogeneous "bubble" solution in which quantum tunnelling occured everywhere at the same time.
639 citations
TL;DR: Very high and broad Curie maxima are observed in ceramic Ba(Ti1-yZry)O3 mixed crystals, which are often used for the preparation of ceramic dielectrics as discussed by the authors.
Abstract: Very high and broad Curie maxima are observed in ceramic Ba(Ti1-yZry)O3 mixed crystals, which are often used for the preparation of ceramic dielectrics The ferroelectric-to-paraelectric phase transition of ceramic Ba(Ti1-yZry)O3 was studied using dielectric measurements, quantitative DTA, X-ray diffraction, and determination of the remanent polarization At higher Zr concentrations, it was found that ferroelectric and paraelectric phases coexist in a wide temperature region Up toy =016, the phase transition remains first order The diffuse character is promoted by the small energy difference between the ferroelectric and paraelectric phases appearing at higher Zr content It can be best described by a normal distribution of Curie temperatures using the phenome-nological theory of Devonshire and the Newton-Raphson mathematical approximation
566 citations
TL;DR: In this paper, it was shown that the Weinberg-salam phase transition is not likely to produce primordial black holes in bubble collisions, but, under certain circumstances, the grand-unified phase transition might give rise to black holes of the order 10 − 3 − 3 g.
Abstract: It is believed that first-order phase transitions occurred in the very early universe when the temperature dropped below the grand-unification and Weinberg-Salam energies. Bubbles of the new, broken-symmetry phase would have formed surrounded by the symmetric phase. The energy released in the phase transition would have caused the walls of the bubbles to accelerate outwards. We study what happens when the walls collide with each other. We find that the energy in the walls would not be thermalized for a considerable time. In the inflationary-universe scenario, in which the bubble nucleation rate is low, thermalization could not occur until long after the baryon and nucleosynthesis eras and would not be complete. We also investigate the formation of primordial black holes in bubble collisions. The Weinberg-Salam phase transition is not likely to produce black holes but, under certain circumstances, the grand-unified phase transition might give rise to black holes of ${10}^{3}$ g.
483 citations
TL;DR: In this paper, an ionized acrylamide gel is found to undergo a discrete phase transition in equilibrium volume upon varying the salt concentration in the solution, which depends strongly on the valency of the positive salt ion added to the solution.
Abstract: An ionized acrylamide gel is found to undergo a discrete phase transition in equilibrium volume upon varying the salt concentration in the solution. The salt concentration required for the transition depends strongly on the valency of the positive salt ion added to the solution. In certain cases the concentration at the transition is many thousand times larger for monovalent ions than for divalent ions. A simple theoretical consideration of the osmotic pressure of the ions can explain the phenomenon.
438 citations
TL;DR: In this paper, the free energy stabilizing the Kondo singlet state is shown to be important in the total energy and stability conditions for cerium and related solids, and explicit calculations are given for the simplest spin-textonehalf{} Kondo model, using the relation to the Anderson Hamiltonian, which leads to a semiquantitative description of the phase transition in cerium.
Abstract: The free energy stabilizing the Kondo singlet state is shown to be important in the total-energy and stability conditions for cerium and related solids. Explicit calculations are given for the simplest spin-\textonehalf{} Kondo model, using the relation to the Anderson Hamiltonian, which leads to a semiquantitative description of the $\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\alpha}$ phase transition in cerium. The temperature dependence of the free energy has a universal form which can lead to a phase boundary terminating in two critical points.
430 citations
411 citations
TL;DR: In this article, the authors used differential scanning calorimetry (DSC) and infrared (IR) spectroscopy to study the solidsolid phase transitions of the odd n-alkanes n-C17H36 through n-c29H60 and found that the concentration of nonplanar conformers successively increases through each phase transition.
Abstract: Solidsolid phase transitions of the odd n-alkanes n-C17H36 through n-C29H60 were studied by using differential scanning calorimetry (DSC) and infrared (IR) spectroscopy. Two phase transitions were found in C25, C2,, and C29 in addition to the previously reported highest-temperature solid-solid transition (the so-called "rotator" transition). IR spectra revealed that, as the temperature is raised, the concentration of nonplanar conformers successively increases through each phase transition. Three types of nonplanar defects have been identified in the highest-temperature phase of all the n-alkanes: "end-gauche" (gt ...), "kink" (...gtg'...), and "double-gauche" (...gg...). The end-gauche defect was observed in the lower-temperature phases as well. Kink conformers, however, were observed only in the highest-temperature phase while double-gauche defects were found in measurable concentrations only within a few degrees of the melting point. The concentrations of nonplanar conformers in the highest-temperature phases increase with increasing chain length. For example, roughly 70% of C29 molcules are nonplanar prior to melting, in contrast to 5-10% for C17. The relationship between the existence of nonplanar conformers and the various distinct solid phases presents a major puzzle. Normal alkanes undergo a remarkable series of solidsolid phase transitions prior to melting. Analogous premelting transitions are also found in a number of more complex systems which contain hydrocarbon chains as major constituents. These systems include polyethylene,' variously substituted alkanes,2 and biological ~nembranes.~ In the latter cases, the phase changes are believed to be intimately related to the state of the hydrocarbon component. For example, current models of the lipid bilayer phase transitions require detailed consideration of the changes in conformation of the alkane chains4 Since the n-alkanes themselves are the sim- plest of these chain-molecule solids, they are a natural starting point for understanding the premelting transitions exhibited by all of these systems. The phase behavior of even the n-alkanes is complex. All odd n-alkanes between C9 and C45 undergo at least one premelting phase transition, and the longer members show no less than four high-temperature solid phases in addition to the low-temperature crystalline phases5 The nature of these phases is not well un- derstood although it is clear that the higher-temperature phases involve increasing degrees of disorder. By disorder here we mean any deviation from the regular arrangement of all-trans chains found in the low-temperature solid. In this paper we focus mainly on one aspect of the disordering processes occurring in these solids-that involving conformational changes. We show that infrared spectroscopy is sensitive to the presence of various nonplanar (not all-trans) conformers and to some types of intermolecular order. We will find that "disorder" occurs in a series of apparently solid phases. The question then arises how can the apparent short-range disorder implied by these nonplanar conformations be reconciled with the existence of a series of phases showing long-range order? This question which is fundamental to the understanding of the more complex systems such as biolipid bilayers will be taken up again in the Conclusion. The body of this paper presents the infrared spectra of the alkanes as a function of temperature with an analysis of the conformational "defects" seen in the various phases.
362 citations
TL;DR: In this article, the scaling behavior of first-order phase transitions is derived from renormalization-group, phenomenological, or finite-size considerations, and it is shown that if the coexistence of distinct phases is possible, then $p$ distinct eigenvalue exponents must equal the spatial dimensionality.
Abstract: Scaling behavior for first-order phase transitions can be derived alternatively but consistently from renormalization-group, phenomenological, or finite-size considerations. A general analysis of densities at a renormalization-group fixed point demonstrates that if the coexistence of $p$ distinct phases is possible, then $p$ distinct eigenvalue exponents must equal the spatial dimensionality. This basic eigenvalue (or scaling) exponent condition can also be derived phenomenologically by various arguments not depending on detailed renormalization-group considerations. A scaling description of first-order phase transitions is presented and extended to finite systems with linear dimensions $L$, leading to a rounding proportional to ${L}^{\ensuremath{-}d}$, response-function maxima varying as ${L}^{d}\ensuremath{\propto}N$, and boundary-condition-dependent shifts which may be as large as $\ensuremath{\sim}{L}^{\ensuremath{-}1}$.
01 Sep 1982
TL;DR: In this article, a model for thermoplastic materials in the process of solid-solid phase transition is presented, where the material is characterized by three different internal state variables: two internal variables which specify the crystallographic structural change during the plastic deformation, and a set of scalar internal variables describing the extent of phase transition.
Abstract: A continuum mechanical description is presented for thermoplastic materials in the process of solid-solid phase transition. The material is assumed to be characterized by three different internal state variables: two internal variables which specify the crystallographic structural change during the plastic deformation, and a set of scalar internal variables which describes the extent of phase transition. Applying Edelen's decomposition theorem, the plastic quantities are determined from the dissipation potential, while the elastic quantities are specified by the internal energy. The explicit form of the flow rule and the evolutional equations for the internal variables are derived. The constitutive equations for the stress and the entropy are obtained in rate-type. It is shown that the continuous cooling transformation (C-C-T) diagram and the isothermal time-temperature-transformation (T-T-T) diagram could be derived from the theory developed here. The infinitesimal case is discussed in detail.
TL;DR: In this article, the authors examined the phase transition properties of nematic liquid crystals aligned by a short-range, arbitrary-strength substrate potential in the framework of Landau-de Gennes theory and showed that the substrate potential not only induces a boundary layer in which the order-parameter values can be significantly different from that of the bulk, but also introduces a new "boundary-layer phase transition" which occurs at temperatures higher than the bulk-transition temperature.
Abstract: Phase-transition properties of nematic liquid crystals aligned by a short-range, arbitrary-strength-substrate potential are examined in the framework of Landau---de Gennes theory. It is shown that the substrate potential, which can arise from surface treatment of liquid-crystal display cells, not only induces a boundary layer in which the order-parameter values can be significantly different from that of the bulk, but also introduces a new "boundary-layer phase transition" which occurs at temperatures higher than the bulk-transition temperature. This novel transition is found to take place only in a limited range of substrate potential strength. For 4-pentyl-4'-cyanobiphenyl (PCB), the limiting values of this range are computed to be \ensuremath{\sim}0.075 and \ensuremath{\sim}0.15 erg/${\mathrm{cm}}^{2}$. Calculations are performed for both the semi-infinite-sample case and the finite-thickness-sample case. Various phase diagrams are presented to show the effects of sample thickness and substrate potential on the bulk as well as the boundary-layer phase-transition temperatures. The paper concludes with a discussion of experimental possibilities.
TL;DR: In this paper, the synthesis and phase behaviour of a series of polymers having liquid crystalline sidechains and a poly(acrylic acid) backbone are described, and a comparison of the phase transitions of the different polyacrylates, with those of liquid-crystalline polymethacryls and polysiloxanes, establishes that the spacer group achieves partial "decoupling" of liquid crystal and polymer properties.
Abstract: The synthesis and phase behaviour of a series of polymers having liquid crystalline sidechains and a poly(acrylic acid) backbone are described. These polymers show a dependence of the phase transition temperatures on molecular weight. In copolymers of two liquid crystalline acrylic esters, induced smectic phases occur. A comparison of the phase transitions of the different polyacrylates, with those of liquid crystalline polymethacrylates and polysiloxanes, published elsewhere, establishes that the spacer group achieves partial “decoupling” of liquid crystalline and polymer properties.
TL;DR: In this article, it was shown that a first order phase transition takes place in KOH-doped ice crystals and that the transition removes most of the residual entropy of the ice crystal.
Abstract: A few crystals exist which have residual entropy1,2. The most notable of these is hexagonal ice, Ih, the ordinary form of solid H2O (ref. 3). The structural interpretation of the residual entropy proposed by Pauling and widely accepted ascribes it to positional disorder of the protons in the ice conditions4. As such a disordered arrangement of the constituent atom cannot be an equilibrium structure of the crystal at the lowest temperature, there has been great interest in the search for a possible ordering phenomenon in ice crystals. We report here a calorimetric experiment which shows that a first order phase transition takes place in KOH-doped ice crystals and that the transition removes most of the residual entropy of the ice crystal.
TL;DR: In this paper, the temperature dependence of the lattice constant in Na0.5Bi 0.5TiO3 single crystal was studied by means of X-ray diffraction and two structural phase transitions were found in the temperature range 293-920 K.
Abstract: The temperature dependence of the lattice constant in Na0.5Bi0.5TiO3 single crystal was studied by means of X-ray diffraction. Two structural phase transitions were found in the temperature range 293-920 K: the cubic-to-tetragonal at 793 ± 5 K and the tetragonal-to-rhombohedral at 533 ± 5 K. The dielectric permittivity was measured and a considerable dispersion was observed. The shift of the dielectric permittivity maximums are linear in coordinates 1/T = F(In f).
TL;DR: In this article, the effects of dislocations on the two-dimensional order of the modulated phases of a uniaxial ferromagnet were investigated using a Ginzburg-Landau approach.
Abstract: A uniaxial ferromagnet of finite thickness spontaneously breaks into parallel "striped" domains as a result of demagnetizing forces. In a sufficiently large applied magnetic field a transition takes place to a hexagonal or "bubble" phase. We study the phase diagram of this system with the use of a Ginzburg-Landau approach and we investigate the effects of dislocations on the two-dimensional order of the modulated phases.
TL;DR: In this article, the existence of spontaneous magnetization at low temperature for the one-dimensional Ising model with 1/r2 interaction energy was proved, and it was shown that the magnetization can be obtained at low temperatures.
Abstract: We prove the existence of a spontaneous magnetization at low temperature for the one-dimensional Ising Model with 1/r2 interaction energy.
TL;DR: In this article, it was shown that the crystal lattice expansion of microcrystalline silicon leads, in the limit of small crystallite size of about 30 A, to an instability of the diamond structure with respect to the amorphous phase.
Abstract: It is shown that the crystal lattice expansion of microcrystalline silicon leads, in the limit of small crystallite size of about 30 A, to an instability of the diamond structure with respect to the amorphous phase. Simple thermodynamic considerations are presented which support the idea of the crystalline-to-amorphous transformation being a discontinuous order—disorder phase transition.
TL;DR: In this paper, the effect of hydrogen and stress on the stability of the austenite phase in stainless steels was investigated using X-ray diffraction and magnetic techniques, and the behavior of two “stable” type AISI310 steels and an “unstable, but still ferromagnetic, type of steel was studied during charging and during the outgassing period following charging.
Abstract: The effect of hydrogen and stress (strain) on the stability of the austenite phase in stainless steels was investigated. Hydrogen was introduced by severe cathodic charging and by elevated temperature equilibration with high pressure H2 gas. Using X-ray diffraction and magnetic techniques, the behavior of two “stable” type AISI310 steels and an “unstable” type AISI304 steel was studied during charging and during the outgassing period following charging. Transformation from the fcc γ phase to an expanded fcc phase, γ*, and to the hcp e phase occurred during cathodic charging. Reversion of the γ* and e phases to the original γ structure and formation of the bcc α structure were examined, and the kinetics of these processes was studied. The γ* phase was shown to be ferromagnetic with a subambient Curie temperature. The γ⇆e phase transition was studied after hydrogen charging in high pressure gas, as was the formation of a during outgassing. These results are interpreted as effects of hydrogen and stress (strain) on the stability of the various phases. A proposed psuedo-binary phase diagram for the metal-hydrogen system was proposed to account for the formation of the γ* phase. The relation of these phase changes to hydrogen embrittlement and stress corrosion cracking of stainless steel is discussed.
TL;DR: In this article, an empirical relation between oxygen-oxygen distance and oxygen-hydrogen distance found widely in various hydrogen-bonded crystals is explained by making use of a simple model potential for hydrogen bond, and some speculation is given on a new interpretation of the isotope effect in ferro or antiferroelectric phase transition temperatures in hydrogen bonded crystals.
Abstract: By making use of a simple model potential for hydrogen bond, empirical relation between oxygen-oxygen distance and oxygen-hydrogen distance found widely in various hydrogen bonded crystals is explained. It is pointed out that, between theoretical prediction and ob served empirical data, there exists a salient discrepancy which is to be resolved by considering quantum effect or tunneling motion of hydrogen atom. The tunneling effect is treated by a variational method on a one dimensional model of hydrogen bond. Possibility of isotope effect in hydrogen bond length is examined and some speculation is given on a new interpretation of the isotope effect in ferro or antiferroelectric phase transition temperatures in hydrogen bonded crystals. In many of the ferroelectrics or antiferroelectrics, the hydrogen bonds con necting two oxygen (or other electronegative) atoms play an important role in their characteristic dielectric behaviours. Particularly when the phase transi tion in these substances is caused by order-disorder arrangements of protons, often is observed a large isotope effect in the. transition temperature Te. This fact manifests itself in that the protons or deuterons in the bonds are crucial elements to trigger the phase transition. Table I is a list of the hydrogen bonded crystals in which ferro (or antiferro) electric phase transitions take place with large isotope effect in Te. As seen from this table, the typical one is KH2 P04 (abbreviated as KDP), where the ratio TeD /Te H is about 1.7. The feature com mon to these hydrogen bonded crystals is the descent of Te with hydrostatic pressure p and the remarkable difference of the slope dTe/dp between for the Table I. The transition temperature Tc and its isotope effect in some ferro and antiferroelectric
TL;DR: In this article, the dynamics of a dilute gas of free spin vortices in a two-dimensional planar magnet were investigated and an equation of motion for the spin vortex was presented and compared with the corresponding equation for a vortex in a superfluid film.
Abstract: We investigate the dynamics of a dilute gas of free spin vortices in a two-dimensional planar magnet. An equation of motion for the spin vortex is presented and compared with the corresponding equation for a vortex in a superfluid film. Exploiting a similar analogy with the dynamics of a two-dimensional plasma in a perpendicular magnetic field we calculate the mean-square vortex velocity and the vortex self-diffusion constant in the critical region above the phase transition. When combined with equations obtained previously for the spin-autocorrelation functions, our results provide an approximate description of the vortex contribution to the critical dynamics outside of the hydrodynamic regime.
TL;DR: In this paper, the ϱ-meson peak was observed to change in the position and width of the peak in very hot fireballs, and the onset of critical behavior might be observable from prompt dilepton production in very fireballs.
TL;DR: In this paper, the phase transition which separates the low-temperature confining phase from the hightemperature nonconfining phase in the SU(3) gauge theory (without quarks) is first order.
Abstract: We argue that the phase transition which separates the low-temperature confining phase from the high-temperature nonconfining phase in the SU(3) gauge theory (without quarks) is first order.
TL;DR: In this paper, an adiabatic scanning calorimeter has been used to study the thermal behavior of the liquid-crystal octylcyanobiphenyl (8CB) in the temperature range between 10 and 50°C.
Abstract: An adiabatic scanning calorimeter has been used to study the thermal behavior of the liquid-crystal octylcyanobiphenyl (8CB) in the temperature range between 10 and 50\ifmmode^\circ\else\textdegree\fi{}C. The solid---to---smectic-$A$ ($\mathrm{KA}$), the smectic-$A$---to---nematic ($\mathrm{AN}$), as well as the nematic-to-isotropic (NI) phase transitions, which fall in this temperature range, have been investigated in great detail. From our measuring procedure the enthalpy behavior (including latent heats) as well as the heat capacity have been obtained. For the KA transition the latent heat was 25.7\ifmmode\pm\else\textpm\fi{}1.0 kJ/mol and for the NI transition it was 612\ifmmode\pm\else\textpm\fi{}5 J/mol. Within the resolution of our experiment we find that the $\mathrm{AN}$ transition is a continuous one. For the latent heat, if any, we arrive at an upper limit of 0.4 J/mol (or 1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ J/g). The observed anomaly in the heat capacity for the $\mathrm{AN}$ transition is not consistent with a nearly logarithmic singularity as predicted by the $\mathrm{XY}$ model, instead we obtain a critical exponent $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=0.31\ifmmode\pm\else\textpm\fi{}0.03$. This result is consistent with the anisotropic scaling relation ${\ensuremath{
u}}_{\ensuremath{\parallel}}+2{\ensuremath{
u}}_{\ensuremath{\perp}}=2\ensuremath{-}\ensuremath{\alpha}$. The pretransitional effects near the NI transition are in qualitative agreement with the hypothesis of quasitricritical behavior.
TL;DR: In this article, the authors estimate the abundance of primordial black holes and their effects on cosmology and show that they play several important roles in the subsequent evolution of the universe and that the observational information of the present universe, conversely, yields constraints on the phenomenological parameters in grand unified theories.
Abstract: One important prediction of a cosmological model based on grand unified theories is the production of primordial black holes and wormholes through a first· order phase transition. In this paper we estimate the abundance of these holes and their effects on cosmology. We show that they play several important roles in the subsequent evolution of the universe and that the observational information of the present universe, conversely, yields constraints on the phenomenological parameters in grand unified theories. Especially we find that both the thermal and quantum nucleations of vacuum bubbles are the necessary ingredients in construct· ing a cosmological model consistent with the present observations.
TL;DR: In this paper, the authors discuss two models of polymer adsorption and give numerical estimates of the locations of phase transition points in the two models, one on a D-dimensional lattice and the other on a 1-dimensional hyperplane.
Abstract: Discusses two models of polymer adsorption. In one model a self-avoiding walk on a D-dimensional lattice interacts with a (D-1)-dimensional hyperplane; in the other model, this walk must also lie in or on one side of this hyperplane. Both models exhibit non-analytic behaviour corresponding to a phase transition, but these phase transitions do not occur at the same point. The authors give numerical estimates of the locations of these transitions.
TL;DR: In this article, the existence of a first-order phase transition in the v-dimensional Potts model for v ≥ 2 when the number of states of a single spin is big enough.
Abstract: We show the existence of a first-order phase transition in thev-dimensional Potts model forv≧2, when the number of states of a single spin is big enough. Low-temperature pure phases are proved to survive up to the critical temperature. Also the existence of a first-order transition in thev-dimensional Potts gauge model,v≧3, is obtained if the underlying gauge group is finite but large.
TL;DR: In this paper, the fractional order beam intensities as well as their angular profiles were recorded as a function of temperature at fixed coverages; they clearly show continuous order-disorder transitions for both hydrogen phases.
TL;DR: The problem of generating ground states of a quenched random Ising spin system with variable concentration of mixed-neighbour exchange couplings on a planar lattice (frustration model) is mapped into the problem of the Chinese postman which has been solved by a polynomial algorithm known as Edmond's algorithm.
Abstract: The problem of generating ground states of a quenched random Ising spin system with variable concentration of mixed-neighbour exchange couplings (Jij()0) on a planar lattice (frustration model) is mapped into the problem of the Chinese postman which has been solved by a polynomial algorithm known as Edmond's algorithm. This algorithm is transposed and applied to the frustration problem. Not only is one particular ground state generated, but a post-optimal algorithm is established which gives the map of the rigid bonds and solidary spins (bonds in the same state for all ground states). This study of the rigidity on a square lattice reveals three distinct regimes by varying x, the concentration of negative bonds: a low-concentration regime where the ground states are rigid and ferromagnetic; an intermediate regime 0.1