Vortex Loop Phase Transitions in Liquid Helium, Cosmic Strings, and High-Tc Superconductors
Gary A. Williams
Abstract
The distribution of thermally excited vortex loops near a superfluid phase transition is calculated from a renormalized theory. The number density of loops with a given perimeter is found to change from exponential decay with increasing perimeter to algebraic decay as Tc is approached, in agreement with recent simulations of both cosmic strings and high-Tc superconductors. Predictions of the value of the exponent of the algebraic decay at Tc and of critical behavior in the vortex density are confirmed by the simulations, giving strong support to the vortex-folding model proposed by Shenoy.
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