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 equations are studied analytically and numerically in many relevant instances, including d=4 and d→∞, with special attention to the critical domain, which is found to correspond to ${\mathrm{\beta }}_{\mathit{c}}$=1/d for all d. Related models (chiral chains) are discussed and large-N solutions are analyzed. © 1996 The American Physical Society.

• Received 21 November 1995

DOI:https://doi.org/10.1103/PhysRevD.53.3230