Chiral phase transition in a random matrix model with three flavors

TL;DR

This paper introduces a modified random matrix model that incorporates the determinant interaction term, accurately capturing the order of chiral phase transitions and the temperature dependence of topological susceptibility for different flavor numbers.

Contribution

A new chiral random matrix model is proposed that includes the determinant interaction term, improving the description of phase transition order and topological susceptibility.

Findings

Second-order transition for N_f=2

First-order transition for N_f=3

Realistic temperature dependence of topological susceptibility

Abstract

The chiral phase transition in the conventional random matrix model is the second order in the chiral limit, irrespective of the number of flavors N_f, because it lacks the U_A(1)-breaking determinant interaction term. Furthermore, it predicts an unphysical value of zero for the topological susceptibility at finite temperatures. We propose a new chiral random matrix model which resolves these difficulties by incorporating the determinant interaction term within the instanton gas picture. The model produces a second-order transition for N_f=2 and a first-order transition for N_f=3, and recovers a physical temperature dependence of the topological susceptibility.