Vortex-ring model of the superfluid lambda transition.

Abstract

An initial model of the superfluid \ensuremath{\lambda} transition is constructed with use of vortex-ring excitations, as originally suggested by Onsager and Feynman. A real-space renormalization technique generates a screened vortex energy and core size, and gives rise to a transition where rings of infinite diameter are excited as the superfluid density approaches zero at ${\mathrm{T}}_{\mathrm{c}}$. Although the model satisfies the Josephson hyperscaling relation, it is not yet a complete theory: The superfluid density exponent is \ensuremath{\nu}=0.53, and does not match the known value \ensuremath{\nu}=0.67.