Renormalization group approach to multiple-arc random matrix models

S. Higuchi; C. Itoi; S. M. Nishigaki; N. Sakai

doi:10.1016/s0370-2693(97)00196-2

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arXiv · hep-th/9612237

Renormalization group approach to multiple-arc random matrix models

S. Higuchi·C. Itoi·S. M. Nishigaki·N. Sakai

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Abstract

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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S. Higuchi, C. Itoi, S. M. Nishigaki, N. Sakai. 1996-12-26. Renormalization group approach to multiple-arc random matrix models. https://doi.org/10.1016/s0370-2693(97)00196-2

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