On the theory of phase transitions in binary fluid mixtures

TL;DR

This paper develops a microscopic theoretical framework for understanding phase transitions in binary fluid mixtures, linking it to the 3D Ising model, and discusses the nature of the order parameter.

Contribution

It introduces a collective variable approach with a reference system to describe phase behavior and critical phenomena in binary mixtures, connecting it to the 3D Ising model.

Findings

Derivation of the Ginzburg-Landau-Wilson Hamiltonian in collective variable space

Reduction of the problem to the 3D Ising model in an external field

Discussion of the physical nature of the order parameter

Abstract

The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order parameter in a binary mixture is discussed. The basic density measure (Ginsburg-Landau-Wilson Hamiltonian) is obtained in the collective variable phase space which contains the variable connected with the order parameter of the system. It is shown that the problem can be reduced to the 3D Ising model in an external field.