Phase diagram of a model for 3He-4He mixtures in three dimensions

TL;DR

This paper investigates a three-dimensional lattice model for 3He-4He mixtures, revealing phase diagrams that align with experimental observations and deriving a continuum Ginzburg-Landau model near tricriticality.

Contribution

It introduces a 3D lattice model incorporating O(2) symmetry and derives a continuum Ginzburg-Landau model with explicit coupling constants.

Findings

Phase diagram resembles experimental data for 3He-4He mixtures.

Superfluid transition leads to phase separation.

Derived continuum model near tricriticality.

Abstract

A lattice model of 3He - 4He mixtures which takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom of 4He is studied in the molecular-field approximation and by Monte Carlo simulations in three dimensions. In contrast to its two-dimensional version, for reasonable values of the interaction parameters the resulting phase diagram resembles that observed experimentally for 3He - 4He mixtures, for which phase separation occurs as a consequence of the superfluid transition. The corresponding continuum Ginzburg-Landau model with two order parameters describing 3He- 4He mixtures near tricriticality is derived from the considered lattice model. All coupling constants appearing in the continuum model are explicitly expressed in terms of the mean concentration of 4He, the temperature, and the microscopic interaction parameters characterizing the lattice system.