Phase diagram of fluid phases in ${}^3$He -${}^4$He mixtures

TL;DR

This paper develops a mean-field lattice gas model for ${}^3$He-${}^4$He mixtures that captures the fluid phase diagram, including vapor phases and superfluid symmetry, to aid in understanding experimental phenomena like tricritical Casimir forces.

Contribution

It introduces a novel lattice gas model incorporating superfluid symmetry and vacancies to describe the phase diagram of helium mixtures.

Findings

Model reproduces fluid phases and vapor coexistence.

Captures superfluid transition with O(2) symmetry.

Provides a framework for experimental Casimir force studies.

Abstract

Fluid parts of the phase diagram of ${}^3$He -${}^4$He mixtures are obtained from a mean-field analysis of a suitable lattice gas model for binary liquid mixtures. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with ${}^4$He and includes the occurrence of vacancies. This latter degree of freedom allows the model to exhibit a vapor phase and hence can provide the theoretical framework to describe the experimental conditions for measurements of tricritical Casimir forces in ${}^3$He -${}^4$He wetting films.