Critical Behavior of Simplicial Chiral 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 $d\to \infty$, 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.

Comments: 47 pages + 4 figures in an uuencoded file