Phase diagrams of a model for two-layerHe3-He4mixture films

Abstract

We present a Migdal-Kadanoff renormalization-group scheme for a model two-layer classical $\mathrm{XY}$ system with annealed impurities. The model Hamiltonian is appropriate for a two-layer ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixture system. We find a rich variety of phase diagrams. Depending on the choice of parameters we find either one or two first-order phase-separation transitions, which may be accompanied by the appearance of superfluidity. Phase diagrams with two $\lambda$ lines are found, making possible two distinct transitions in the superfluid density. In the case of phase-separation transitions, each transition is primarily associated with a single layer, and three-phase coexistence is possible. Comparison with recent experiments is made.