Extreme-Value Distributions and the Freezing Transition of Structural Glasses

TL;DR

This paper links extreme-value statistics to the freezing transition in structural glasses, showing different EVS distributions govern fluctuations in two mean-field models, revealing a novel connection between EVS and glass physics.

Contribution

It demonstrates that the finite-size fluctuations of the freezing temperature in mean-field glass models follow specific EVS distributions, with analytical insights into the Tracy-Widom distribution emergence.

Findings

REM freezing temperature fluctuations follow Gumbel EVS

PSM fluctuations follow Tracy-Widom EVS

Analytical explanation for TW distribution in PSM

Abstract

We consider two mean-field models of structural glasses, the random energy model (REM) and the $p$-spin model (PSM), and we show that the finite-size fluctuations of the freezing temperature are described by extreme-value statistics (EVS) distributions, establishing an unprecedented connection between EVS and the freezing transition of structural glasses. For the REM, the freezing-temperature fluctuations are described by the Gumbel EVS distribution, while for the PSM the freezing temperature fluctuates according to the Tracy-Widom (TW) EVS distribution, which has been recently discovered within the theory of random matrices. For the PSM, we provide an analytical argument showing that the emergence of the TW distribution can be understood in terms of the statistics of glassy metastable states.