Unitary Matrix Models and Phase Transition

TL;DR

This paper investigates the phase structure of a unitary matrix model with a topological theta term, revealing how the dominance of the theta or Wilson term affects the existence of phase transitions.

Contribution

It demonstrates the conditions under which the topological phase transition appears or disappears depending on the relative strength of the theta and Wilson terms.

Findings

Phase transition at λ_c=2 in the symmetric model.

Transition persists if Wilson term exceeds theta term.

Transition disappears when theta term dominates.

Abstract

We study the unitary matrix model with a topological term. We call the topological term the theta term. In the symmetric model there is the phase transition between the strong and weak coupling regime at $\lambda_{c}=2$. If the Wilson term is bigger than the theta term, there is the strong-weak coupling phase transition at the same $\lambda_{c}$. On the other hand, if the theta term is bigger than the Wilson term, there is only the strong coupling regime. So the topological phase transition disappears in this case.