VARIATIONAL MASTER FIELD FOR LARGE-N INTERACTING MATRIX MODELS - FREERANDOM-VARIABLES ON TRIAL

Matrices are said to behave as flee non-commuting random variables if the action which governs their dynamics constrains only their eigenval ues, i.e. depends on traces of powers of individual matrices. The auth ors use recently developed mathematical techniques in combination with a standard variational principle to formulate a new variational appro ach for matrix models. Approximate variational solutions of interactin g large-N matrix models are found using the free random matrices as th e variational space. Several classes of classical and quantum mechanic al matrix models with different types of interactions are considered a nd the variational solutions compared with exact Monte Carlo and analy tical results. Impressive agreement is found in a majority of cases. ( C) 1997 Elsevier Science B.V.