Dynamics of dilute disordered models: a solvable case

TL;DR

This paper investigates the dynamics of a dilute spherical disordered model with random interactions, revealing a crossover temperature and two asymptotic regimes, and compares its behavior to real glasses.

Contribution

It introduces a functional variational method for analyzing dilute disordered models and characterizes their dynamic regimes and spectral properties.

Findings

Identification of a crossover temperature replacing the dynamic transition

Two asymptotic regimes linked to spectral density and localized configurations

Comparison of model behavior with real glass dynamics

Abstract

We study the dynamics of a dilute spherical model with two body interactions and random exchanges. We analyze the Langevin equations and we introduce a functional variational method to study generic dilute disordered models. A crossover temperature replaces the dynamic transition of the fully-connected limit. There are two asymptotic regimes, one determined by the central band of the spectral density of the interactions and a slower one determined by localized configurations on sites with high connectivity. We confront the behavior of this model to the one of real glasses.