PHASE-DIAGRAM OF A MODEL FOR HE-3-HE-4 MIXTURES IN 2 DIMENSIONS

A dilute two-dimensional classical X-Y model is proposed to describe two-dimensional He3-He4 mixtures. Using a Villain form for the potential, a Migdal-Kadanoff position-space renormalization is carried out. The resulting phase diagram plotted against T and the He3 concentration x, is qualitatively similar to that for a three-dimensional mixture with some important differences: (i) The initial phase separation is into two normal fluids having different concentrations of He3 rather than into a normal fluid and a superfluid, so there is no real tricritical point. (ii) At lower temperatures, the phase separation is into a superfluid and a normal fluid, and as the phase-separation temperature is approached from the normal side, islands of superfluid appear, with the correlation length diverging with an exponent ν=1. © 1979 The American Physical Society.