UA(1) breaking and phase transition in chiral random matrix model

TL;DR

This paper introduces a chiral random matrix model that captures the flavor-number dependence of (1) symmetry breaking and phase transitions, revealing different orders for two and three massless flavors and analyzing topological susceptibility behavior.

Contribution

The model uniquely incorporates flavor-number dependence of (1) anomaly effects on phase transitions in chiral systems.

Findings

Second-order phase transition for two massless flavors with mean-field exponents.

First-order phase transition for three massless flavors.

Topological susceptibility decreases with increasing temperature.

Abstract

We propose a chiral random matrix model which properly incorporates the flavor-number dependence of the phase transition owing to the \UA(1) anomaly term. At finite temperature, the model shows the second-order phase transition with mean-field critical exponents for two massless flavors, while in the case of three massless flavors the transition turns out to be of the first order. The topological susceptibility satisfies the anomalous \UA(1) Ward identity and decreases gradually with the temperature increased.