Is there a Glass Transition in Planar Vortex Systems?

TL;DR

This paper investigates the existence of a glass transition in planar vortex systems with quenched disorder, finding that such systems are likely glassy at all temperatures unless a finite vortex persistence length is considered.

Contribution

The study provides an exact analysis of the free energy and stiffness in planar vortex systems, revealing conditions under which a glass transition occurs or is absent.

Findings

System is glassy at all temperatures when vortex persistence length approaches zero.

A finite vortex persistence length introduces a glass transition.

Results align with numerical simulations of related models.

Abstract

The criteria for the existence of a glass transition in a planar vortex array with quenched disorder are studied. Applying a replica Bethe ansatz, we obtain for self-avoiding vortices the exact quenched average free energy and effective stiffness which is found to be in excellent agreement with recent numerical results for the related random bond dimer model [1]. Including a repulsive vortex interaction and a finite vortex persistence length \xi, we find that for \xi \to 0 the system is at {\em all} temperatures in a glassy phase; a glass transition exists only for finite \xi. Our results indicate that planar vortex arrays in superconducting films are glassy at presumably all temperatures.