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

Abstract

We propose a chiral random matrix model which properly incorporates the flavor-number dependence of the phase transition owing to the ${\mathrm{U}}_{\mathrm{A}}(1)$ 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 ${\mathrm{U}}_{\mathrm{A}}(1)$ Ward identity and decreases gradually with the temperature increased.