Dynamical phase transition in the activity-biased fully-connected random field Ising model: connection with glass-forming systems

TL;DR

This paper investigates how biasing the activity in a fully-connected random-field Ising model induces dynamical phase transitions, revealing connections to glass transition theories and showing symmetry-breaking phenomena.

Contribution

It introduces a mean-field analysis of activity-biased trajectories in the RFIM, uncovering new dynamical phases and symmetry-breaking transitions.

Findings

Identification of dynamical phase transitions under activity bias.

Observation of spontaneous symmetry breaking into ordered states.

Connection of results to glass-forming system theories.

Abstract

We analyse biased ensembles of trajectories for the random-field Ising model on a fully-connected lattice, which is described exactly by mean-field theory. By coupling the activity of the system to a dynamical biasing field, we find a range of dynamical phase transitions, including spontaneous symmetry breaking into ordered states. For weak bias, the phase behaviour is controlled by extrema of the free energy, which may be local minima or saddle points. For large bias, the system tends to states of extremal activity, which may differ strongly from free energy minima. We discuss connections of these results to random first-order transition theory of glasses, which motivates an extension of the analysis to random-field Ising models where the dynamical activity is not symmetric under magnetisation reversal.