The chiral phase transition, random matrix models, and lattice data

TL;DR

This paper provides evidence that the microscopic spectral density of the Dirac operator is universal, supported by lattice data comparisons and random matrix models that incorporate finite temperature effects and Matsubara frequencies.

Contribution

It introduces a random matrix model for the chiral phase transition that includes all Matsubara frequencies, extending previous models.

Findings

Lattice data matches random matrix theory predictions.

Microscopic spectral correlations are temperature-independent.

A new random matrix model captures the chiral phase transition with finite temperature effects.

Abstract

We present two pieces of evidence in support of the conjecture that the microscopic spectral density of the Dirac operator is a universal quantity. First, we compare lattice data to predictions from random matrix theory. Second, we show that the functional form of the microscopic spectral correlations remains unchanged in random matrix models which take account of finite temperature. Furthermore, we present a random matrix model for the chiral phase transition in which all Matsubara frequencies are included.