Pressure-temperature phase diagrams of selenium and sulfur in terms of Patashinski model

The pressure - temperature phase diagrams of Se and S are calculated. Both melting and polymorphous phase transition are described in the frames of statistical Patashinski model. The results are in good agreement with experimental data of Brazhkin et. al.Comment: 3 eps figures, will appear in Physica A, mail to first author [email protected]

Nonequilibrium Critical Phenomena

We discuss the non-equilibrium critical phenomena in liquids, and the models for these phenomena based on local equilibrium and extended scaling assumptions. Special situations are proposed for experimental tests of the theory. Near-critical steady and transient states are reviewed. In a near-critical steady state characterized by a temperature gradient, the theory predicts strong nonequilibrium fluctuations at very large length scales. Close to the critical point, this results in a nonlinear regime of heat conductivity. A transient non-equilibrium state triggered by a rapid and large spatially uniform perturbation of the critical liquid is considered. A step away from criticality generates a free field with strong and decaying correlations in initial state, while a step towards criticality initiates the increase of fluctuations and of their correlation at the large scale edge of the critical range. The approach to equilibrium is characterized by an equilibration length \Lambda_eq that depends on time t. The theory predicts a power law approach of the temperature to the new equilibrium; the new critical exponents depend on whether the temperature is initially increased or decreased

Anomalous fluctuations in phases with a broken continuous symmetry

It is shown that the Goldstone modes associated with a broken continuous symmetry lead to anomalously large fluctuations of the zero field order parameter at any temperature below T_c. In dimensions 2<d<4, the variance of the extensive spontaneous magnetization scales as L^4 with the system size L, independent of the order parameter dynamics. The anomalous scaling is a consequence of the 1/q^{4-d} divergence of the longitudinal susceptibility. For ground states in two dimensions with Goldstone modes vanishing linearly with momentum, the dynamical susceptibility contains a singular contribution (q^2-\omega^2/c^2)^{-1/2}. The dynamic structure factor thus exhibits a critical continuum above the undamped spin wave pole, which may be detected by neutron scattering in the N\'eel-phase of 2D quantum antiferromagnets.Comment: final version, minor change

Surface rearrangement at complex adsorbate-substrate interfaces

On the basis of the information theory approach we propose a novel statistical scheme for analyzing the evolution of coupled adsorbate-substrate systems, in which the substrate undergoes the adsorbate-induced transformations. A relation between the substrate morphology and the adsorbate thermodynamic state is established. This allows one to estimate the surface structure in terms of incomplete experimental information and the one concerning the adsorbate thermodynamic response to the structural modifications.Comment: 5 pages, 3 figure

Probability Density, Diagrammatic Technique, and Epsilon Expansion in the Theory of Wave Turbulence

We apply the methods of Field Theory to study the turbulent regimes of statistical systems. First we show how one can find their probability densities. For the case of the theory of wave turbulence with four-wave interaction we calculate them explicitly and study their properties. Using those densities we show how one can in principle calculate any correlation function in this theory by means of direct perturbative expansion in powers of the interaction. Then we give the general form of the corrections to the kinetic equation and develop an appropriate diagrammatic technique. This technique, while resembling that of $\varphi^4$ theory, has many new distinctive features. The role of the $\epsilon=d-4$ parameter is played here by the parameter $\kappa=\beta + d - \alpha - \gamma$ where $\beta$ is the dimension of the interaction, $d$ is the space dimension, $\alpha$ is the dimension of the energy spectrum and $\gamma$ is the ``classical'' wave density dimension. If $\kappa > 0$ then the Kolmogorov index is exact, and if $\kappa < 0$ then we expect it to be modified by the interaction. For $\kappa$ a small negative number, $\alpha<1$ and a special form of the interaction we compute this modification explicitly with the additional assumption of the irrelevance of the IR divergencies which still needs to be verified.Comment: 26 pages, PUPT-146

The free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a variety of other spin systems generally assumed to belong to the same critical universality class. In particular, we have also derived the analogous expansions for the Ising models with spin s=1,3/2,.. and for the lattice euclidean scalar field theory with quartic self-interaction, on the simple cubic and the body-centered cubic lattices. Our bivariate high-temperature expansions, which extend through K^24, enable us to compute, through the same order, all higher derivatives of the free energy with respect to the field, namely all higher susceptibilities. These data make more accurate checks possible, in critical conditions, both of the scaling and the universality properties with respect to the lattice and the interaction structure and also help to improve an approximate parametric representation of the critical equation of state for the three-dimensional Ising model universality class.Comment: 22 pages, 10 figure