Matrix model approach to the flux lattice melting in $2D$ superconductors

TL;DR

This paper models flux lattice melting in 2D superconductors using a gauged matrix model, analyzing phase transitions via saddle point methods and exploring the connection to superconductor fluctuations.

Contribution

It introduces a large N gauged matrix model approach to study flux lattice melting and identifies a critical point related to phase transition behavior.

Findings

Critical coupling constant g_c identified

Phase transition linked to flux lattice melting

Free energy expanded up to eighth order

Abstract

We investigate a gauged matrix model in the large $N$ limit which is closely related to the superconductor fluctuation and the flux lattice melting in two dimensions. With the use of saddle point method the free energy is expanded up to eighth order for the coupling constant $g$. In the case that the coefficient of quadratic term of the Ginzburg-Landau matrix model is negative, a critical point $g=g_c$ is obtained in the large $N$ limit and the relation between this phase transition and the 2D flux lattice melting transition is discussed.