Renormalization-group approach to superfluidity and other metastable phases

Abstract

The Landau-Ginzburg-Wilson field-theoretical approach to study the critical equilibrium properties of metastable superfluid phases of He II, superconductors and metastable helical magnetic configurations of $\mathrm{XY}$ ferromagnets is presented. Under the assumption that nucleation processes are absent, the perturbation rules for the thermal fluctuations are derived. In spite of the fact that the internal, rotational, and translational symmetries are spontaneously broken, a residual symmetry left over permits the introduction of a modified momentum space, in which Feynman rules are simple and Green's functions are readily calculable. The renormalization-group equations satisfied by the new correlation functions are obtained, and their general solutions are evaluated at a fixed point. The equation of state relating the temperature, the modulus of the order parameter, the superfluid velocity or helix pitch, and, in the case of a ferromagnet, an external magnetic field is derived. This equation satisfies a generalized scaling form and reduces to the traditional Widom expression when the superfluid velocity tends to zero. The equation is calculated to order $\ensuremath{\epsilon}=4\ensuremath{-}d$ in the loop expansion. Several physical consequences of these results are presented.