On matrix model partition functions for QCD with chemical potential

TL;DR

This paper compares two matrix models for QCD with chemical potential, demonstrating their universality and analyzing the chiral phase transition with respect to flavor content and chemical potential.

Contribution

It provides a detailed comparison of two matrix models for QCD with chemical potential, confirming their universality and analyzing phase transitions for various flavor configurations.

Findings

Complete agreement between models in the large-N limit at weak nonhermiticity.

Agreement for equal quark and conjugate flavors at strong nonhermiticity.

First order chiral phase transition at critical chemical potential.

Abstract

Partition functions of two different matrix models for QCD with chemical potential are computed for an arbitrary number of quark and complex conjugate anti-quark flavors. In the large-N limit of weak nonhermiticity complete agreement is found between the two models. This supports the universality of such fermionic partition functions, that is of products of characteristic polynomials in the complex plane. In the strong nonhermiticity limit agreement is found for an equal number of quark and conjugate flavours. For a general flavor content the equality of partition functions holds only for small chemical potential. The chiral phase transition is analyzed for an arbitrary number of quarks, where the free energy presents a discontinuity of first order at a critical chemical potential. In the case of nondegenerate flavors there is first order phase transition for each separate mass scale.