DESCRIPTION OF CRITICAL BEHAVIOUR OF MODEL SYSTEMS USING NON-GAUSSIAN MEASURES (YUKHNOVSKII'S APPROACH)

Kozlovskii Kozlovskii,Patsahan Patsahan

doi:10.5488/cmp.3.3.607

Abstract

We present a brief review of the works devoted to a study of critical phenomena in three-dimensional model systems dwelling on the Yukhnovskii approach in detail. This approach which is based on the use of non-Gaussian measures allows one to obtain both universal and non-universal quantities. In order to illustrate the advantages of the approach proposed by I.R.Yukhnovskii we apply it to a study of non-universal quantities, namely: (1) the phase transition temperature of a 3D one-component lattice model, (2) the gas-liquid critical point properties of fluid systems.

Highlights

A description of phase transitions as well as critical phenomena connected with them remains a relevant problem
In this work we present some results of the latest calculations of non-universal characteristics for statistical models of the phase transition in the critical region using the approach proposed by I.Yukhnovskii [11]
We present the main aspects of the collective variables (CV) method with a reference system for a multi-component continuous system in the grand canonical ensemble (GCE) as well as some results for simple and binary fluids obtained using the Yukhnovskii approach

Summary

Introduction

A description of phase transitions as well as critical phenomena connected with them remains a relevant problem. The following and basic constituent of Yukhnovskii’s approach is the way of calculating the partition function near the phase transition point This original calculation method [24] as well as Wilson’s approach exploit the renormalization group (RG) ideas, it is based on the use of the non-Gaussian measures. Hereafter we apply the Yukhnovskii approach to the description of non-universal quantities, namely: (1) the phase transition temperature for a 3D one-component lattice model, (2) the gas-liquid critical point properties both of a one-component fluid and a binary mixture. This method is based on the Wilson approach [8] which consists in the layer-by-layer calculation of a partition function by means of the successive exclusion of short-wave-length fluctuations from consideration This is the realization of the Kadanoff idea of the construction of effective block lattices described in detail in [9]. Within the framework of a unified scheme one can perform the calculation of the full expressions for thermodynamic functions and obtain both universal and non-universal characteristics of the model under consideration

Calculation of the partition function

A one-component fluid

A binary fluid mixture

Gas-liquid critical temperature of the symmetrical square-well mixture