Equilibrium Fluctuations in Mean-field Disordered Models

TL;DR

This paper develops a comprehensive analytical framework to quantify equilibrium fluctuations in mean-field glass models, validated by numerical simulations, and identifies finite-size corrections crucial for understanding these complex systems.

Contribution

It introduces a fully quantitative method using the replica approach to evaluate Gaussian fluctuations in mean-field disordered models, extending previous critical scaling studies.

Findings

Analytical results match numerical simulations for p-spin and orthogonal models.

Decomposition of fluctuations into thermal and heterogenous components.

Provides a scheme to identify finite-size corrections in glass models.

Abstract

Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for all equilibrium conditions. By means of the replica method we evaluate Gaussian fluctuations of the overlaps around the thermodynamic limit, decomposing them in thermal fluctuations inside each state and heterogeneous fluctuations between different states. We first test and compare our analytical results with numerical simulation results for the p-spin spherical model and the random orthogonal model, and then analyze the random Lorentz gas. In all cases, a strong quantitative agreement is obtained. Our analysis thus provides a robust scheme for identifying the key finite-size (or finite-dimensional) corrections to the mean-field treatment of these paradigmatic glass models.