Universality in the level statistics of disordered systems

TL;DR

This paper investigates the universal behavior of energy level statistics in disordered systems, showing that high disorder entropy leads to spectra resembling a random energy model, regardless of specific system details.

Contribution

It demonstrates the universality of spectral behavior in disordered systems, particularly the transition to random energy model spectra when disorder entropy exceeds dynamical entropy.

Findings

Spectra become similar to a random energy model under high disorder entropy.

The observed spectral universality applies broadly across different disordered systems.

The Edwards-Anderson model exemplifies this transition.

Abstract

Energy spectra of disordered systems share a common feature: if the entropy of the quenched disorder is larger than the entropy of the dynamical variables, the spectrum is locally that of a random energy model and the correlation between energy and configuration is lost. We demonstrate this effect for the Edwards-Anderson model, but we also discuss its universality.