Glassy Critical Points and Random Field Ising Model

TL;DR

This paper demonstrates that the critical points of continuous glass transitions in constrained liquids can be modeled by the Random Field Ising Model, supported by analytical and numerical finite size scaling analysis.

Contribution

It establishes a mapping between the critical replica field theory of glass transitions and the $\,\phi^4$-Random Field Ising Model, providing new insights into glass criticality.

Findings

The critical replica field theory maps onto the RFIM.

Finite size scaling confirms the continuous transition in the $p$-spin model.

Analytical and numerical results support the RFIM description.

Abstract

We consider the critical properties of points of continuous glass transition as one can find in liquids in presence of constraints or in liquids in porous media. Through a one loop analysis we show that the critical Replica Field Theory describing these points can be mapped in the $\phi^4$-Random Field Ising Model. We confirm our analysis studying the finite size scaling of the $p$-spin model defined on sparse random graph, where a fraction of variables is frozen such that the phase transition is of a continuous kind.