An Approximate Large $N$ Method for Lattice Chiral Models

TL;DR

This paper introduces an approximate method to solve lattice chiral models that accurately predicts phase transitions and reproduces known large N results, providing insights into the models' behavior across different dimensions.

Contribution

It presents a new approximate large N method for lattice chiral models that explicitly solves Schwinger-Dyson equations and predicts phase transitions.

Findings

Correctly predicts phase transition for d > 2

System is disordered with a mass gap for d ≤ 2

Reproduces known N=∞ results well for d=1

Abstract

An approximation is used that permits one to explicitly solve the two-point Schwinger-Dyson equations of the U(N) lattice chiral models. The approximate solution correctly predicts a phase transition for dimensions $d$ greater than two. For $d \le 2 $, the system is in a single disordered phase with a mass gap. The method reproduces known $N=\infty$ results well for $d=1$. For $d=2$, there is a moderate difference with $N=\infty$ results only in the intermediate coupling constant region.