More on generalized simplicial chiral models

TL;DR

This paper extends simplicial chiral models by generalizing the auxiliary field term, solving specific cases analytically, and revealing a third-order phase transition similar to 2D Yang-Mills theory.

Contribution

It introduces a generalized class of simplicial chiral models and analytically solves the d=0 and d=2 cases at large-N, showing phase transition behavior.

Findings

Eigenvalue density function in strong regime for d=0

Partition function consistency with path integral

Third order phase transition in d=2 models

Abstract

By generalizing the auxiliary field term in the Lagrangian of simplicial chiral models on a (d-1)-dimensional simplex, the generalized simplicial chiral models has been introduced in \c{Ali}. These models can be solved analytically only in d=0 and d=2 cases at large-N limit. In d=0 case, we calculate the eigenvalue density function in strong regime and show that the partition function computed from this density function is consistent with one calculated by path integration directly. In d=2 case, it is shown that all $V= {\rm Tr}(AA^{\d})^n$ models have a third order phase transition, same as the 2-dimensional Yang-Mills theory.