Critical Behavior of Simplicial Chiral Models

TL;DR

This paper investigates the critical behavior of simplicial chiral models in the large-N limit, deriving saddle-point equations and analyzing their solutions across various dimensions, revealing a universal critical point at =1/d.

Contribution

It derives and analyzes large-N saddle-point equations for simplicial chiral models on a d-1 simplex, providing new insights into their critical behavior across dimensions.

Findings

Critical point at =1/d for all dimensions

Analytical and numerical solutions of saddle-point equations

Discussion of related chiral chain models

Abstract

The large-N saddle-point equations for the principal chiral models defined on a d-1 dimensional simplex are derived from the external field problem for unitary integrals. The saddle point equation are studied analytically and numerically in many relevant instances, including d=4 and $d\rightarrow\infty$, with special attention to the critical domain, which is found to correspond to $\beta_c=1/d$ for all d. Related models (chiral chains) are discussed and large-N solutions are analyzed.