Finite size effects in a mean-field kinetically constrained model: dynamical glassiness and quantum criticality

TL;DR

This paper studies finite-size effects in a mean-field kinetically constrained model, revealing how classical dynamical transitions relate to quantum criticality and characterizing finite-size behavior of the order parameter.

Contribution

It demonstrates a mapping between classical dynamical phase transitions and quantum first-order transitions to analyze finite-size effects.

Findings

Finite-size scaling of the order parameter is characterized.

Classical dynamical transition properties are analogous to quantum first-order transitions.

The quantum analogy provides a new way to analyze finite-size effects in glassy systems.

Abstract

On the example of a mean-field Fredrickson-Andersen kinetically constrained model, we focus on the known property that equilibrium dynamics take place at a first-order dynamical phase transition point in the space of time-realizations. We investigate the finite-size properties of this first order transition. By discussing and exploiting a mapping of the classical dynamical transition -an argued glassiness signature- to a first-order quantum transition, we show that the quantum analogy can be exploited to extract finite-size properties, which in many respects are similar to those in genuine mean-field quantum systems with a first-order transition. We fully characterize the finite-size properties of the order parameter across the first order transition.