Masses and Phase Structure in the Ginzburg-Landau Model

TL;DR

This study numerically investigates the phase structure of the Ginzburg-Landau model, focusing on mass measurements, revealing a phase transition marked by photon mass vanishing, with different orders for type I and II superconductors.

Contribution

It provides new numerical evidence on the nature of phase transitions and mass behavior in the Ginzburg-Landau model, especially regarding photon and scalar masses.

Findings

Photon mass vanishes at the phase transition.

Type I superconductors exhibit a first-order transition.

Type II superconductors show signs of second-order critical behavior.

Abstract

We study numerically the phase structure of the Ginzburg-Landau model, with particular emphasis on mass measurements. There is no local gauge invariant order parameter, but we find that there is a phase transition characterized by a vanishing photon mass. For type I superconductors the transition is of 1st order. For type II 1st order is excluded by susceptibility analysis, but the photon correlation length suggests 2nd order critical behaviour with \nu ~ 1/2. The scalar mass, in contrast, does not show clear critical behaviour in the type II regime for V \to \infty, contrary to the conventional picture.