Monte Carlo simulations of the XY vectorial Blume-Emery-Griffiths model in multilayer films for ^{3}He-^{4}He mixtures.

Abstract

The XY vectorial generalization of the Blume-Emery-Griffiths (XY-VBEG) model, which is suitable to be applied to the study of ^{3}He-^{4}He mixtures, is treated on thin films structure and its thermodynamical properties are analyzed as a function of the film thickness. We employ extensive and up-to-date Monte Carlo simulations consisting of hybrid algorithms combining lattice-gas moves, Metropolis, Wolff, and super-relaxation procedures to overcome the critical slowing down and correlations among different spin configurations of the system. We also make use of single histogram techniques to get the behavior of the thermodynamical quantities close to the corresponding transition temperatures. Thin films of the XY-VBEG model present a quite rich phase diagram with Berezinskii-Kosterlitz-Thouless (BKT) transitions, BKT endpoints, and isolated critical points. As one varies the impurity concentrations along the layers, and in the limit of infinite film thickness, there is a coalescence of the BKT transition endpoint and the isolated critical point into a single, unique tricritical point. In addition, when mimicking the behavior of thin films of ^{3}He-^{4}He mixtures, one obtains that the concentration of ^{3}He atoms decreases from the outer layers to the inner layers of the film, meaning that the superfluid particles tend to locate in the bulk of the system.