Vortex Loop Phase Transitions in Liquid Helium, Cosmic Strings, and High-T_c Superconductors

TL;DR

This paper investigates vortex loop phase transitions in superfluid helium, cosmic strings, and high-temperature superconductors, showing how vortex loop distributions change near critical temperatures and confirming theoretical predictions with simulations.

Contribution

It provides a renormalized theoretical calculation of vortex loop distributions near phase transitions, validating the vortex-folding model through simulation comparisons.

Findings

Vortex loop distribution shifts from exponential to algebraic decay near T_c.

Predicted algebraic decay exponent matches simulation results.

Critical vortex density behavior is confirmed by simulations.

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 T_c is approached, in agreement with recent simulations of both cosmic strings and high-T_c superconductors. Predictions of the value of the exponent of the algebraic decay at T_c and of critical behavior in the vortex density are confirmed by the simulations, giving strong support to the vortex-folding model proposed by Shenoy.