Vortices and the Ginzburg-Landau phase transition

TL;DR

This paper discusses how vortex loops influence the phase transition in Ginzburg-Landau superconductivity, using lattice Monte Carlo simulations and gauge-invariant observables to connect lattice results with continuum physics.

Contribution

It introduces gauge-invariant measures of vortex loops and establishes exact relations between lattice and continuum quantities for studying phase transitions.

Findings

Vortex loops play a crucial role in the Ginzburg-Landau phase transition.

Gauge-invariant observables enable accurate extrapolation to the continuum limit.

The relationship between symmetry breaking and phase transitions is clarified.

Abstract

The methods for studying the role of vortex loops in the phase transition of the Ginzburg-Landau theory of superconductivity using lattice Monte Carlo simulations are discussed. Gauge-invariant observables that measure the properties of the vortex loop distribution are defined. The exact relations between the lattice and continuum quantities make it possible to extrapolate the results of the simulations to the continuum limit. The relationship between spontaneous symmetry breaking and phase transitions is also reviewed, with an emphasis on the fact that a local symmetry cannot be broken.