RENORMALIZATION-GROUP APPROACH TO MULTIPLE-ARC RANDOM-MATRIX MODELS

We study critical and universal behaviors of unitary invariant non-gau ssian random matrix ensembles within the framework of the large-N reno rmalization group. For a simple double-well model we find an unstable fixed point and a stable inverse-gaussian fixed point. The former is i dentified as the critical point of single/double-arc phase transition with a discontinuity of the third derivative of the free energy. The l atter signifies a novel universality of large-N correlators other than the usual single are type. This phase structure is consistent with th e universality classification of two-level correlators for multiple-ar c models by Ambjorn and Akemann. We also establish the stability of th e gaussian fixed point in the multi-coupling model. (C) 1997 Elsevier Science B.V.