Matrix models as solvable glass models

TL;DR

This paper introduces a family of high-dimensional particle interaction models, including matrix and tensor models, exhibiting glassy behavior and aging effects, with detailed analysis for the matrix case.

Contribution

It presents a new class of solvable models without quenched disorder, bridging matrix and tensor models, and analyzes their glassy dynamics.

Findings

Models exhibit glassy regimes with aging effects

Analytical and numerical study of matrix models for p=2

Extension to tensor models for p>2

Abstract

We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter $p$. For $p=2$ we obtain matrix models and for $p>2$ `tensor' models. We concentrate on the cases $p=2$ which we study analytically and numerically.