Renormalization group approach to multiple-arc random matrix models

Details Renormalization group approach to multiple-arc random matrix models Renormalization group approach to multiple-arc random matrix models

1996-12-26

arxiv.org/abs/hep-th/9612237v1

Phys.Lett. B398 (1997) 123-129

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 1 figure, LaTeX + a4.sty, epsf.sty

Scientific paper

10.1016/S0370-2693(97)00196-2

We study critical and universal behaviors of unitary invariant non-gaussian random matrix ensembles within the framework of the large-N renormalization group. For a simple double-well model we find an unstable fixed point and a stable inverse-gaussian fixed point. The former is identified as the critical point of single/double-arc phase transition with a discontinuity of the third derivative of the free energy. The latter signifies a novel universality of large-N correlators other than the usual single arc type. This phase structure is consistent with the universality classification of two-level correlators for multiple-arc models by Ambjorn and Akemann. We also establish the stability of the gaussian fixed point in the multi-coupling model.

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