Finite size scaling analysis of the glass transition

TL;DR

This paper demonstrates that finite size scaling methods can effectively analyze the glass transition by identifying a diverging correlation length and employing a new parameter to locate the transition precisely.

Contribution

It introduces a novel finite size scaling approach and a parameter B(T,L) for accurately determining the glass transition in lattice models and potentially other systems.

Findings

Finite size scaling techniques successfully locate the glass transition.

A new parameter B(T,L) effectively captures transition dependences.

The approach applies broadly to glass-forming systems.

Abstract

We show that finite size scaling techniques can be employed to study the glass transition. Our results follow from the postulate of a diverging correlation length at the glass transition whose physical manifestation is the presence of dynamical heterogeneities. We introduce a parameter B(T,L) whose temperature, T, and system size, L, dependences permit a precise location of the glass transition. We discuss the finite size scaling behaviour of a diverging susceptibility \chi(L,T). These new techniques are successfully used to study two lattice models. The analysis straightforwardly applies to any glass-forming system.