Fragile-glass behavior of a short range $p$-spin model

TL;DR

This paper introduces a short-range p-spin model to explore glassy dynamics, revealing fragile glass behavior, super-Arrhenius relaxation, and an entropy-driven transition consistent with experimental observations.

Contribution

It proposes a new short-range p-spin model and demonstrates its ability to reproduce key features of fragile glasses through simulations.

Findings

Fragile glass behavior with stretched exponential relaxation.

Super-Arrhenius and Vogel-Fulcher relaxation times.

No growth in correlation length despite increasing relaxation times.

Abstract

In this paper we propose a short range generalization of the $p$-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom-line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We however encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin glass susceptibility investigating the behavior of the correlation length in the system. We find that the the increase of the relaxation time is not accompanied by any growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory.