Finite size scaling analysis of the glass transition

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.