Vortex-Loop Phase Transitions in Liquid Helium, Cosmic Strings, and High-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Superconductors

Abstract

The distribution of thermally excited vortex loops near a superfluid phase\ntransition is calculated from a renormalized theory. The number density of\nloops with a given perimeter is found to change from exponential decay with\nincreasing perimeter to algebraic decay as T_c is approached, in agreement with\nrecent simulations of both cosmic strings and high-T_c superconductors.\nPredictions of the value of the exponent of the algebraic decay at T_c and of\ncritical behavior in the vortex density are confirmed by the simulations,\ngiving strong support to the vortex-folding model proposed by Shenoy.\n