Renormalization group approach to multiple-arc random matrix models

TL;DR

This paper applies the renormalization group framework to analyze critical phenomena and universality in non-Gaussian random matrix models, revealing fixed points and phase transitions with implications for multi-arc spectral structures.

Contribution

It introduces a renormalization group approach to study phase transitions and universality in multi-arc random matrix models, identifying fixed points and novel universality classes.

Findings

Identified an unstable fixed point as the critical point of phase transition.

Discovered a stable inverse-Gaussian fixed point indicating new universality.

Confirmed the stability of the Gaussian fixed point in multi-coupling models.

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.