Rare-event trajectory ensemble approach to study dynamical phase transitions in the zero temperature Glauber model

TL;DR

This paper introduces a rare-event trajectory ensemble approach to analyze dynamical phase transitions in a one-dimensional stochastic particle system, revealing both continuous and discontinuous transitions through analytical and numerical methods.

Contribution

It develops a novel trajectory ensemble method combined with large deviation theory to identify dynamical phase transitions in the zero temperature Glauber model.

Findings

Identification of continuous and discontinuous dynamical phase transitions.

Exact analytical results for infinite systems.

Numerical confirmation of analytical predictions.

Abstract

The dynamics of a one-dimensional stochastic system of classical particles consisting of asymmetric death and branching processes is studied. The dynamical activity, defined as the number of configuration changes in a dynamical trajectory, is considered as a proper dynamical order parameter. By considering an ensemble of dynamical trajectories and applying the large deviation method, we have found that the system might undergo both continuous and discontinuous dynamical phase transitions at critical values of the counting field. Exact analytical results are obtained for an infinite system. Numerical investigations confirm our analytical calculations.