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

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.

32 pages, 12 figures, submitted to the Phys. Rev. E

References in corpus (3)

• Cluster Hybrid Monte Carlo Simulation Algorithms
• Critical Casimir effect and wetting by helium mixtures
• Generalized-ensemble simulations of spin systems and protein systems

Cited by in corpus (15)

• Monte Carlo study of an improved clock model in three dimensions
• Critical Casimir Effect in superfluid wetting films
• Probability Distribution Function of the Order Parameter: Mixing Fields and Universality
• Critical Casimir Effect in 3He-4He films
• XY Spin Fluid in an External Magnetic Field
• First order phase transitions in classical lattice gas spin models
• Monte Carlo Study of an Inhomogeneous Blume-Capel Model
• Anomalies in the Multicritical Behavior of Staggered Magnetic and Direct Magnetic Susceptibilities of Iron Group Dihalides
• The tricritical Ising CFT and conformal bootstrap
• Miscibility regimes in a ${}^{23}$Na-${}^{39}$K quantum mixture
• Phase diagram of fluid phases in ${}^3$He -${}^4$He mixtures
• Emergent tri-criticality in magnetic metamaterials
• Critical $1$- and $2$-point spin correlations for the $O(2)$ model in $3d$ bounded domains
• Tricritical Casimir forces and order parameter profiles in wetting films of ${}^3\text{He}$ -${}^4\text{He}$ mixtures
• Tricriticality of the Blume-Emery-Griffiths Model In Thin Films of Stacked Triangular Lattices