Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling

TL;DR

This paper clarifies how the nature of phase coexistence in discontinuous phase transitions determines whether finite-size scaling follows exponential or power-law behavior, resolving conflicting reports in the literature.

Contribution

It introduces a classification of discontinuous phase transitions based on phase coexistence, linking these classes to their distinct dynamical scaling behaviors using large deviation theory.

Findings

Phase coexistence leads to exponential scaling due to stochastic switching.

Absence of phase coexistence results in power-law scaling from diffusive relaxation.

The classification explains conflicting observations in previous studies.

Abstract

There are conflicting reports in the literature regarding the finite-size scaling of the Liouvillian gap and dynamical fluctuations at discontinuous phase transitions, with various studies reporting either exponential or power-law behavior. We clarify this issue by employing large deviation theory. We distinguish two distinct classes of discontinuous phase transitions that have different dynamical properties. The first class is associated with phase coexistence, i.e., the presence of multiple stable attractors of the system dynamics (e.g., local minima of the free energy functional) in a finite phase diagram region around the phase transition point. In that case, one observes asymptotic exponential scaling related to stochastic switching between attractors (though the onset of exponential scaling may sometimes occur for very large system sizes). In the second class, there is no phase coexistence away from the phase transition point, while at the phase transition point itself there are infinitely many attractors. In that case, one observes power-law scaling related to the diffusive nature of the system relaxation to the stationary state.