SUPERFLUIDITY AND PHASE-SEPARATION IN HELIUM FILMS

A vectorial generalization of the Blume-Emery-Griffiths model is proposed to describe superfluidity in films of He3-He4 mixtures, and is solved by an approximate renormalization scheme due to Migdal. In contrast to bulk mixtures, the line of superfluid transitions is connected to the phase-separation curve by a critical end point. The universal jump of the superfluid density, present in the pure He4 system, is preserved with increasing He3 concentrations x until the critical end point occurs at xa0.12. At smaller x, phase separation causes a kink in the superfluid density versus temperature curve. No tricritical point occurs for any value of the model parameters, although an effectively tricritical phase diagram is obtained in a certain limit. Lines of constant superfluid density bunch up near the effective tricritical point, as predicted by tricritical scaling theory. This treatment also describes superfluidity in pure He4 films in the presence of two-dimensional liquid-gas phase separation. In addition we calculate the specific heat of the pure He4 system, using the recursion relations of Kosterlitz. This specific heat has a broad maximum above the superfluid transition temperature, corresponding to a gradual dissociation of vortex pairs with increasing temperature. © 1979 The American Physical Society.