Monte Carlo study of a vortex glass model

TL;DR

This paper uses Monte Carlo simulations to study a vortex glass model, revealing a finite transition temperature in four dimensions and no finite temperature transition in two dimensions, shedding light on disordered superconductor behavior.

Contribution

It provides the first detailed Monte Carlo analysis of a vortex glass model across different dimensions, highlighting the dimensional dependence of the phase transition.

Findings

Finite transition temperature in 4D

Transition at zero temperature in 2D

Finite-size scaling analysis confirms results

Abstract

We describe results of Monte Carlo simulations on a model that seems to have the necessary ingredients to describe a disordered type-II superconductor in a magnetic field. We compute the free energy cost to twist the direction of the phase of the condensate and analyze the results by finite-size scaling. The results show convincingly that the model has different behavior as a function of dimension: in $d=4$ the model clearly has a finite transition temperature; $T_c$, while for $d=2$ only there is only a transition at $T=0$.