The Ising M-p-spin mean-field model for the structural glass: continuous vs. discontinuous transition

TL;DR

This paper analyzes the critical behavior of the $M-p$ Ising spin glass model, revealing a crossover between continuous and discontinuous phase transitions, with implications for understanding structural glasses.

Contribution

It introduces a family of mean-field models that interpolate between different types of phase transitions and are extendable to finite-dimensional systems.

Findings

Crossover between continuous and first-order transitions

Model's microscopic properties allow extension to finite dimensions

Provides insights into structural glass behavior

Abstract

The critical behavior of a family of fully connected mean-field models with quenched disorder, the $M-p$ Ising spin glass, is analyzed, displaying a crossover between a continuous and a random first order phase transition as a control parameter is tuned. Due to its microscopic properties the model is straightforwardly extendable to finite dimensions in any geometry.