Universality Classes of Critical Points in Constrained Glasses

TL;DR

This paper classifies the universality classes of critical points in constrained glasses, revealing Ising and RFIM classes depending on the type of constraint, and provides predictions for correlation functions that can be tested numerically.

Contribution

It establishes the universality classes of critical points in constrained glasses using replica field theory, distinguishing between Ising and RFIM classes based on the nature of the constraints.

Findings

Critical points in symmetric coupling are in the Ising universality class.

Coupling with an equilibrium reference or frozen particles leads to RFIM universality class.

Predictions for correlation function behavior can be tested in simulations.

Abstract

We analyze critical points that can be induced in glassy systems by the presence of constraints. These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in absence of constraints. Through a deep analysis of the soft modes appearing in the replica field theory we can establish the universality class of these points. In the case of the "annealed potential" of a symmetric coupling between two copies of the system, the critical point is in the Ising universality class. More interestingly, is the case of the "quenched potential" where the a single copy is coupled with an equilibrium reference configuration, or the "pinned particle" case where a fraction of particles is frozen in fixed positions. In these cases we find the Random Field Ising Model (RFIM) universality class. The effective random field is a "self-generated" disorder that reflects the random choice of the reference configuration. The RFIM representation of the critical theory predicts non-trivial relations governing the leading singular behavior of relevant correlation functions, that can be tested in numerical simulations.