An Approximate Large $N$ Method for Lattice Chiral Models

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.