Renormalization-group study of superfluidity and phase separation of helium mixtures immersed in a disordered porous medium

Abstract

Superfluidity and phase separation in ${}^{3}{\mathrm{H}\mathrm{e}\ensuremath{-}}^{4}\mathrm{He}$ mixtures immersed in aerogel are studied by renormalization-group theory. The quenched disorder imposed by aerogel, both at the atomic level and at the geometric level, is included. The calculation is conducted via the coupled renormalization-group mappings, near and away from aerogel, of the quenched probability distributions of random interactions. Random-bond effects on the onset of superfluidity and random-field effects on superfluid-superfluid phase separation are seen. The quenched randomness causes the \ensuremath{\lambda} line of second-order phase transitions of superfluidity onset to reach zero temperature, in agreement with general predictions and experiments. The effects of the atomic and geometric randomness of aerogel are investigated separately and jointly.