Large-N phase transitions in the spectrum of products of complex matrices

TL;DR

This paper explores phase transitions in the spectral properties of products of complex matrices in the large-N limit, revealing a transition from perturbative to nonperturbative regimes marked by a nonanalytic point.

Contribution

It extends the understanding of large-N phase structures from unitary matrices to complex matrices, identifying a phase transition in their spectral behavior.

Findings

Identification of a phase transition point in the spectrum

Generalization of large-N phase structure to complex matrices

Existence of a nonanalyticity at the transition point

Abstract

It is shown that the simplest multiplicative random complex matrix model generalizes the large-N phase structure found in the unitary case: A perturbative regime is joined to a nonperturbative regime at a point of nonanalyticity.