The two-dimensional twisted reduced principal chiral model revisited

TL;DR

This paper revisits the two-dimensional twisted reduced principal chiral model, demonstrating it reproduces key features of the standard model and analyzing its large N phase transition as first order.

Contribution

It shows that the reduced matrix model accurately captures the continuum limit and phase transition properties of the standard principal chiral model.

Findings

Reproduces continuum limit features such as internal energy and mass gap

Identifies the large N phase transition as first order

Extends analysis to larger N values for phase transition study

Abstract

Motivated by our previous study of the Twisted Eguchi-Kawai model for non minimal twists, we re-examined the behaviour of the reduced version of the two dimensional principal chiral model. We show that this single matrix model reproduces the same features as the standard lattice model. In particular, scaling towards the continuum limit, the correct value of the internal energy, the magnetic susceptibility and the mass gap. Given our capacity to reach larger values of $N$, we use the reduced model to study the nature and properties of its large $N$ phase transition existing at intermediate coupling. We conclude that the transition is of first order