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.

Latex file, 19 pages

References in corpus (5)

• A Study of U(N) Lattice Gauge Theory in 2-dimensions
• On the $0^{++}$ Glueball Mass
• Two dimensional SU(N) x SU(N) chiral models on the lattice
• Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function
• Strong-coupling expansion of chiral models