Universality in p-spin glasses with correlated disorder

TL;DR

This paper demonstrates that the low temperature phase of p-spin glasses remains universal under correlated non-Gaussian disorder, using advanced random tensor theory techniques.

Contribution

It introduces a new method based on random tensor theory to establish universality in p-spin glasses with correlated disorder, extending known results.

Findings

Universality holds for correlated non-Gaussian disorder

Critical temperature is affected by correlations

Method applies to finite-range models

Abstract

We introduce a new method, based on the recently developed random tensor theory, to study the p-spin glass model with non-Gaussian, correlated disorder. Using a suitable generalization of Gurau's theorem on the universality of the large N limit of the p-unitary ensemble of random tensors, we exhibit an infinite family of such non-Gaussian distributions which leads to same low temperature phase as the Gaussian distribution. While this result is easy to show (and well known) for uncorrelated disorder, its robustness with respect to strong quenched correlations is surprising. We show in detail how the critical temperature is renormalized by these correlations. We close with a speculation on possible applications of random tensor theory to finite-range spin glass models.