Showing papers on "Phase transition published in 1984"

Volume phase transition in a nonionic gel

Abstract: Nonionic N‐isopropylacrylamide gel was found to undergo a discontinuous phase transition by changing a solvent composition or temperature. The observation that polymer gel with and without charge can undergo a first order volume phase transition is an evidence for the universality of the phase transition of polymer gels.

Universal features of the equation of state of metals

Abstract: The zero-temperature equation of state of metals, in the absence of phase transitions, is shown to be accurately predicted from zero-pressure data. Upon appropriate scaling of experimental pressure-volume data a simple universal relation is found. These results provide further experimental confirmation of the recent observation that the total-binding-energy---versus---separation relations for metals obey a universal scaling relation. Important to our results is a parameter $\ensuremath{\eta}$, which is a measure of the anharmonicity of a crystal. This parameter is shown to be essential in predicting the equation of state. A simple formula is given which predicts the zero-temperature derivative of the bulk modulus with respect to pressure.

Remarks on the chiral phase transition in chromodynamics

Abstract: The phase transition restoring chiral symmetry at finite temperatures is considered in a linear $\ensuremath{\sigma}$ model. For three or more massless flavors, the perturbative $\ensuremath{\epsilon}$ expansion predicts the phase transition is of first order. At high temperatures, the ${\mathrm{U}}_{A}(1)$ symmetry will also be effectively restored.

Dynamics of supercooled liquids and the glass transition

Abstract: Closed nonlinear equations are derived for a self-consistent treatment of density propagation, self-diffusion and current relaxation in a classical monatomic fluid. The solution for a hard-sphere model system brings out a phase transition to a glass at the packing fraction 0.516. Approaching the transition from the glass side the particle mean-square displacement increases to a finite value. A simplified model is analysed in detail. Approaching the transition from the liquid side the diffusivity is predicted to decrease to zero with a power law with exponent 1.76 which the authors find to agree well with some experimental data. The low-frequency density spectrum is found to consist of two contributions; one is an elastic line of the frozen structure on the glass side, which then decays to a narrow diffusion broadened quasielastic peak on the fluid side; the other part is described by a dynamical scaling law and it yields in particular a spectrum diverging at the glass point with certain exponents.

Walks, walls, wetting, and melting

Abstract: New results concerning the statistics of, in particular,p random walkers on a line whose paths do not cross are reported, extended, and interpreted. A general mechanism yielding phase transitions in one-dimensional or linear systems is recalled and applied to various wetting and melting phenomena in (d=2)-dimensional systems, including fluid films and p×1 commensurate adsorbed phases, in which interfaces and domain walls can be modelled by noncrossing walks. The heuristic concept of an effective force between a walk and a rigid wall, and hence between interfaces and walls and between interfaces, is expounded and applied to wetting in an external field, to the behavior of the two-point correlations of a two-dimensional Ising model belowTc and in a field, and to the character of commensurate-incommensurate transitions ford=2 (recapturing recent results by various workers). Applications of random walk ideas to three-dimensional problems are illustrated in connection with melting in a lipid membrane model.

Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors

Abstract: We investigate theoretically and via computer simulation the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external fieldE. The effect of the field is to bias jumps in the field direction and thus produce a current carrying steady state. Simulations on a periodic 30 × 30 square lattice with attractive nearest-neighbor interactions suggest a nonequilibrium phase transition from a disordered phase to an ordered one, similar to the para-to-ferromagnetic transition in equilibriumE=0. At low temperatures and largeE the system segregates into two phases with an interface oriented parallel to the field. The critical temperature is larger than the equilibrium Onsager value atE=0 and increases with the field. For repulsive interactions the usual equilibrium phase transition (ordering on sublattices) is suppressed. We report on conductivity, bulk diffusivity, structure function, etc. in the steady state over a wide range of temperature and electric field. We also present rigorous proofs of the Kubo formula for bulk diffusivity and electrical conductivity and show the positivity of the entropy production for a general class of stochastic lattice gases in a uniform electric field.

Structured phase transitions on a finite interval

Abstract: : VAN DER WAALS, in his classic paper, gave arguments in support of a compressible fluid whose free energy at constant temperature depends not only on the density, but also on the density gradient. CAHN & HILLIARD, apparently unaware of VAN DER WAALS' paper, rederived VAN DER WAALS' theory and, using this theory, obtained several important results concerning the interfacial energy between phases. Since then gradient theories have been used to analyze phase transitions, spinodal decomposition, and other physical phenomena.

Phase Transition of the Two-Dimensional Heisenberg Antiferromagnet on the Triangular Lattice

Abstract: Ordering process of the antiferromagnetic Heisenberg model on the two-dimensional triangular lattice is studied both by topological analysis of defects and by Monte Carlo simulation. It is shown that the order parameter space of this model is isomorphic to the three-dimensional rotation group SO(3) due to the inherent frustration effect. Homotopy analysis shows that the system bears a topologically stable point defect characterized by a two-valued topological quantum number and exhibits a phase transition driven by the dissociation of the vortices. A Monte Carlo study on the specific heat and the behavior of vortices strongly suggests the occurence of a Kosterlitz-Thouless-type phase transition. It is, however, argued that in contrast to the two-dimensional X Y model, the spin-correlation function decays exponentially even in the low-temperature phase. In order to distinguish the high- and low-temperature phases qualitatively, we introduce a “vorticity function” analogously to the Wilson loop in the quark...

Structural study on ferroelectric phase transition of vinylidene fluoride-trifluoroethylene copolymers (III) dependence of transitional behavior on VDF molar content

Abstract: Structural changes occurring in the ferroelectric phase transition of vinylidene fluoride-trifluoroethylene (VDF-TrFE) copolymers with the various VDF molar contents have been investigated by means of X-ray diffraction and infrared spectroscopic methods. The phase transition occurs among three crystal phases of the low-temperature (regular all-trans conformation), the high-temperature (gauche conformation with a large rotational motion), and the cooled phases (disordered trans conformation). In the copolymer with low VDF molar content less than 40%, the broad transition between the cooled phase and the high-temperature phase is observed and the conformational change from trans to gauche is not so perfect. In the range of VDF 50–60%, the transition becomes more definite, and on the way of heating the low-temperature phase transforms to the cooled phase, which transfers continuously to the high-temperature phase. For copolymers of VDF 70–80%, a clear and discontinuous first order transition between...

Nature of the Phase Transition of the Two-Dimensional Antiferromagnetic Plane Rotator Model on the Triangular Lattice

Abstract: A study is made on the antiferromagnetic plane rotator model on the triangular lattice by Monte Carlo simulations In sharp contrast to the ferromagnetic case the specific heat shows a logarithmic divergence at a critical temperature and the magnetic susceptibility is almost independent of temperature over a wide temperature range The origin of the divergent specific heat is ascribed to an order-disorder transition of chirality, which is introduced to characterize the two-fold degeneracy of the ground state A discussion is made on the possible existence of an intermediate phase, in which the translational spin order vanishes, but the chirality order remains

Ferroelectrics with diffuse phase transition

Abstract: The results of an investigation of a large group of diffuse phase transition ferroelectrics distinguished by a number of specific features that make them important for both research and application are reported. A mechanism for diffuse phase transition is proposed. The necessity of a theory for this class of disordered and non-equilibrium systems is pointed out.

Infrared spectroscopy in KNbO3 through the successive ferroelectric phase transitions

Abstract: The temperature dependence of the infrared reflectivity spectra in KNbO3 is reported for the cubic, tetragonal and orthorhombic phases in a temperature range extending from 300 to 1200K. Spectra have been fitted with a model based on the factorised form of the dielectric function. The temperature dependence of the mode frequencies, the dampings and the oscillator strengths through the successive phase transitions is reported. The experimental data exhibit an unstable mode which decreases continuously in frequency upon cooling across the diverse transitions. The ionic effective charges, the spontaneous polarisation and the static dielectric constant are calculated from these data. All results are discussed in terms of a displacive/order-disorder crossover, which appears especially when the transition from the cubic to the tetragonal phase is approached. A particular phase transition mechanism is proposed, which leads to an understanding of the discrepancy between the experimental and the calculated values of the dielectric constant, the large damping of the soft mode, the incomplete softening of the unstable phonon and the special sequence of phase transitions.

Modulated, or long-periodic, magnetic structures of crystals

Abstract: The experimental results on modulated magnetic structures and the basic regularities of phase transitions between them are reviewed and are analyzed on the basis of the phenomenological theory of phase transitions with the use of the Ginzburg-Landau functionals for inhomogeneous distributions of the order parameter. Lists of presently known crystals, in which modulated magnetic structures have been observed, are presented and for many of them the form of these functionals, taking into account the crystalline anisotropy and the interaction with a magnetic field, is established. For systems admitting a Lifshitz invariant which is linear with respect to the gradient, a soliton picture of the structure of the incommensurate phase is established and the phase transition into the commensurate phase under the action of temperature or a magnetic field is analyzed. It is shown that this transition is accompanied by a "locking" of the wave vector to the commensurate value. For systems without Lifshitz invariants, which include most crystals with modulated structures, nonlinear equations for the distribution of the order parameter are investigated by asymptotic methods, and these solutions permit describing the entire complex of observed phenomena: the temperature and field dependence of the wave vector, the appearance of higher-order satellites in the neutron duffraction pattern, and the sequence of magnetic phases. Thus a systematic and complete exposition of the present experimental and theoretical status of long-periodic magnetic structures of crystals, such as the spiral structure, the longitudinal and transverse spin-wave structures, the fan structure, and others, is given in this review. The review is written so as to be accessible and of interest to a wide range of readers who are interested in both the theoretical and experimental aspects of the study of magnetic phase transitions in crystals.

Linear optical birefringence of magnetic crystals

Abstract: The study of changes in the refractive indices (with consequent changes of birefringence) of a transparent magnetic crystal which accompany changes in the magnetic order is becoming more popular. The authors review why this is. The first reason is that birefringence can be measured very accurately: the different experimental arrangements are reviewed. The second reason is because a birefringence measurement is an integrational spectroscopic technique and therefore it is studied both experimentally and theoretically as a branch of magneto-optics and hence gives information on the detailed energy level structure of the solid. The third reason is that in a number of interesting systems the birefringence is proportional to the magnetic energy over a wide temperature range and it is often a more convenient method of obtaining the magnetic specific heat than direct specific heat measurements; this is particularly true in magnetic crystals which show low dimensional ordering. The last reason is that in all magnetic crystals the birefringence change should vary like one of the thermodynamic critical exponents near to the phase transition. They review in detail the reasons why birefringence studies have become so successful for measuring critical exponents in pure and particularly mixed crystals.

Bistable systems: Master equation versus Fokker-Planck modeling

Abstract: Relaxation and fluctuations of nonlinear macroscopic systems, which are frequently described by means of Fokker-Planck or Langevin equations, are studied on the basis of a master equation. The problem of an approximate Fokker-Planck modeling of the dynamics is investigated. A new Fokker-Planck modeling is presented which is superior to the conventional method based on the truncated Kramers-Moyal expansion. The new approach is shown to give the correct transition rates between deterministically stable states, while the conventional method overestimates these rates. An application to the Schl\"ogl models for first- and second-order nonequilibrium phase transitions is given.

Computer Studies of Phase Transitions and Critical Phenomena

Abstract: 1. Introduction.- 2. Computer Methods in the Study of Phase Transitions and Critical Phenomena.- 2.1 Statistical Mechanics and Phase Transitions.- 2.1.1 Modern theories of phase transitions and critical phenomena.- 2.1.2 Statistical mechanics, order parameters, fluctuations, critical exponents, scaling, and universality.- 2.2 Numerical Simulation Techniques.- 2.2.1 Monte Carlo methods.- 2.2.2 A Monte Carlo importance-sampling method.- 2.2.3 A realization of a Monte Carlo method.- 2.2.4 General limitations of the Monte Carlo method.- 2.2.5 Broken ergodicity.- 2.2.6 Distribution functions.- 2.2.7 Coarse-graining techniques and criteria of convergence.- 2.2.8 Finite-size effects.- 2.2.9 Determining the nature of a phase transition.- 2.2.10 Computational details.- 2.2.11 General advantages of the Monte Carlo method: Applications.- 2.3 Exact Configurational Counting and Series Expansions.- 2.3.1 A general approach.- 2.3.2 The moment method.- 2.3.3 Principles of the calculation.- 2.3.4 Step 1. Determination of all distinct graphs and their multiplicities.- 2.3.5 Step 2. Embedding of connected graphs into a lattice.- 2.3.6 General correlation function series.- 2.3.7 Capabilities and limitations of a general approach.- 3. Monte Carlo Pure-model Calculations.- 3.1 Critical Behavior of the Three-dimensional Ising Model.- 3.1.1 The Ising model and its order parameter.- 3.1.2 Numerical evidence of a phase transition in the Ising model on a diamond lattice.- 3.1.3 Finite-size scaling analysis and critical behavior.- 3.1.4 Are Monte Carlo techniques practicable in the study of critical phenomena?.- 3.2 Phase Behavior of Ising Models with Multi-spin Interactions.- 3.2.1 Higher-order exchange in magnetic systems.- 3.2.2 Ising models with multi-spin interactions.- 3.2.3 First-order phase transitions of Ising models with pure multi-spin interactions.- 3.2.4 Universality and tricritical behavior of Ising models with two- and four-spin interactions: Pair interactions as a symmetry-breaking field.- 3.3 Thermodynamics of One-dimensional Heisenberg Models.- 3.3.1 One-dimensional magnetic models.- 3.3.2 The anisotropic Heisenberg model in a magnetic field.- 3.3.3 Comparison with theoretical calculations on a continuum model.- 3.3.4 A model ofthe linear magnet CsNiF3?.- 4. Testing Modern Theories of Critical Phenomena.- 4.1 Fluctuation-induced First-order Phase Transitions.- 4.1.1 The role of fixed points in the renormalization group theory.- 4.1.2 Motivation for computer studies of fluctuation-induced first-order phase transitions.- 4.1.3 Phase transitions in antiferromagnets with order Parameters of dimension n=6 and n=3.- 4.1.4 Crossover from first-order to continuous transitions in a symmetry-breaking field.- 4.1.5 Fluctuation-induced first-order phase transitions in Ising models with competing interactions.- 4.2 Critical Phenomena at Marginal Dimensionality.- 4.2.1 The role of a marginal spatial dimension.- 4.2.2 Computer experiments of hypercubic Ising models: ?A romance of many dimensions?.- 4.2.3 Susceptibility and critical isotherm of the four-dimensional Ising model.- 4.2.4 Conclusions on critical behavior in marginal dimensions.- 4.3 Basic Assumptions of Critical Correlation Theories.- 4.3.1 Review of a critical correlation theory.- 4.3.2 Testing the basic assumption by Monte Carlo calculations.- 5. Numerical Experiments.- 5.1 Phase Transitions in Lipid Bilayers and Biological Membranes.- 5.1.1 What are biological membranes and what do they do?.- 5.1.2 Lipid bilayers are model membranes.- 5.1.3 Phase behavior of lipid bilayers.- 5.1.4 Back to biology: Are phase transitions at all relevant to the biological functions of the membrane?.- 5.1.5 Theories of lipid bilayer phase transitions.- 5.1.6 Computer simulations of lipid bilayers.- 5.1.7 Multi-state models of lipid bilayers.- 5.1.8 Computer simulations of the q-state models for the gel-fluid phase transition.- 5.1.9 Computer Simulation of the phase behavior of lipid bilayers with ?impurities?: cholesterol, proteins, and Polypeptides.- 5.1.10 Have Computer studies provided any new insight into the properties of biological membranes?.- 5.2 Nuclear Dipolar Magnetic Ordering and Phase Transitions.- 5.2.1 Nuclear dipolar magnetic ordering.- 5.2.2 The secular dipolar Hamiltonian.- 5.2.3 Perspectives in studies of nuclear dipolar magnetic ordering.- 5.2.4 Motivation for a numerical Simulation study of nuclear dipolar magnetic ordering.- 5.2.5 Monte Carlo studies of systems with truncated classical secular dipolar interactions.- 5.2.6 Nature of the spin structures: ?Permanent? structures or the devil's staircase?.- 5.2.7 Double-layered spin structures in CaF2-like systems: Continuous transitions and critical behavior.- 5.2.8 Multi-layered spin structures in CaF2-like systems: Firstorder phase transitions.- 5.2.9 Can series expansions provide information on the nature of the phase transitions?.- 5.2.10 Nuclear antiferrimagnetic susceptibilities of systems with two spin species: LiF and LiH.- 5.3 Phase Transitions of Adsorbed Monolayers.- 5.3.1 Two-dimensional phases of molecules adsorbed on solid surfaces.- 5.3.2 N2 physisorbed on graphite: The anisotropic-planar rotor model.- 5.3.3 The Heisenberg model with cubic anisotropy.- 5.3.4 Fluctuation-induced first-order phase transition in the anisotropic-planar rotor model.- 5.3.5 Comparison with experiments on N2 physisorbed on graphite.- 5.3.6 Phase behavior on the anisotropic-planar rotor model with vacancies.- 5.3.7 Physical realizations of the anisotropic-planar rotor model with vacancies.- 5.4 Kinetics of Growth.- 5.4.1 Growth.- 5.4.2 Computer Simulation of domain-growth kinetics.- 5.4.3 Domain-growth kinetics of herringbonephases.- 5.4.4 Domain-growth kinetics of pinwheel phases.- 5.4.5 Kinetics of growth and critical phenomena.

Experimental evidence for a liquid - gas phase transition in nuclear systems

Abstract: At certain combinations of temperature and density, nuclear matter may exist as a liquid-gas mixture exhibiting phase instabilities, a characteristic signature of which may be found in the emission of intermediate-mass fragments in nuclear collisions. The present analysis of fragment distributions from proton- and heavy-ion-induced reactions, in the framework of a theory of condensation, is suggestive of the occurrence of such phase transitions with a critical exponent $k\ensuremath{\sim}1.7$ and a critical temperature ${T}_{c}\ensuremath{\sim}12$ MeV.

Si-III (BC-8) crystal phase of Si and C: Structural properties, phase stabilities, and phase transitions

Abstract: With use of the pseudopotential local-density-functional approach, the lattice constant, the $x$ parameter for atomic coordinates, and the phonon frequency of the mode ${\ensuremath{\Gamma}}_{1}^{+}$ are calculated for the Si-III (BC-8) crystal phases of Si and Ci. The results agree well with available experimental data for the BC-8 phases of Si. From the total-energy curves of the diamond and the BC-8 phases of Si, we find that the BC-8 phase of Si is not stable at ambient pressure or at high pressure. The diamond---BC-8 (I-III) transition of Si will not occur quasistatically. Comparing the diamond, the BC-8, and the simple-cubic phases of C, we find that diamond will first transform to the BC-8 phase at 12 Mbar and then to the simple-cubic phase at 27 Mbar under quasistatic conditions.

Equilibrium crystal shapes for lattice models with nearest-and next-nearest-neighbor interactions

Abstract: Equilibrium crystal shapes for a three-dimensional ferromagnetic Ising model with both nearest-neighbor (${J}_{1}$) and next-nearest-neighbor (${J}_{2}=R{J}_{1}$) interactions are studied at nonzero temperatures. Phase diagrams and crystal shapes are first calculated via mean-field theory. Subsequently, fluctuation corrections are taken into account in a qualitative manner, incorporating known results and exploiting interconnections with other ($d=2$) models, including both roughening and commensurate-incommensurate phase transitions. In the resulting picture, crystal facets appear only below appropriate roughening temperatures. Phase boundaries correspond directly to edges bounding crystal facets and may be either first order (slope discontinuity, sharp edges) or second order (no slope discontinuity, smooth edges). For $R\ensuremath{\ge}0$, only smooth edges occur, and phase transitions are of the Gruber-Mullins\char22{}Pokrovsky-Talapov type. For $Rl0$ additional, first-order phase transitions take place at sufficiently low temperatures.

Unified Description of Static and Dynamic Scaling for Kinetic Cluster Formation

Abstract: A scaling theory is developed for aggregation by means of kinetic clustering of clusters. A global picture of static and dynamic critical properties emerges, whereby the dynamic critical exponent can be related to the fractal dimension. Furthermore, the growth process is described in terms of a purely kinetic model. The scaling predictions agree well with numerical results.