Abstract
Models of unitary matrices are solved exactly in a double scaling limit, using orthogonal polynomials on a circle. Exact differential equations are found for the scaling functions of these models. For the simplest model (k=1), the Painlevé II equation with constant 0 is obtained. There are possible nonperturbative phase transitions in these models. The scaling function is of the form ×f((-λ)) for the kth multicritical point. The specific heat is , and is therefore manifestly positive. Equations are given for k=2 and 3, with a discussion of asymptotic behavior.
- Received 20 December 1989
DOI:https://doi.org/10.1103/PhysRevLett.64.1326
©1990 American Physical Society