Are Mean-Field Spin-Glass Models Relevant for the Structural Glass Transition?

TL;DR

This paper investigates finite-size fully connected p-spin models and finds they exhibit properties similar to real super-cooled liquids near the glass transition, supporting their relevance as statistical models.

Contribution

It demonstrates that finite-size p-spin-like models with activated processes mirror real glassy behavior, validating their use in studying the glass transition.

Findings

Finite-size p-spin models show glassy properties near transition.

Models exhibit activated processes similar to real liquids.

Results support models as relevant for super-cooled liquid studies.

Abstract

We analyze the properties of the energy landscape of {\it finite-size} fully connected p-spin-like models whose high temperature phase is described, in the thermodynamic limit, by the schematic Mode Coupling Theory of super-cooled liquids. We show that {\it finite-size} fully connected p-spin-like models, where activated processes are possible, do exhibit properties typical of real super-cooled liquid when both are near the critical glass transition. Our results support the conclusion that fully-connected p-spin-like models are the natural statistical mechanical models for studying the glass transition in super-cooled liquids.