Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model

TL;DR

This paper investigates the finite-size effects of a first-order dynamical phase transition in a one-dimensional model, using advanced numerical methods and an effective theory to understand its behavior.

Contribution

It introduces a multi-canonical feedback control in the cloning algorithm and develops an effective model to analyze the phase transition.

Findings

Improved numerical efficiency with multi-canonical feedback control.

Quantitative agreement between the effective theory and numerical results.

Insights applicable to broader classes of dynamical phase transitions.

Abstract

We analyze large deviations of the time-averaged activity in the one dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large deviation function. We analyze the finite-size scaling of this phase transition numerically, by generalizing an existing cloning algorithm to include a multi-canonical feedback control: this significantly improves the computational efficiency. Motivated by these numerical results, we formulate an effective theory for the model in the vicinity of the phase transition, which accounts quantitatively for the observed behavior. We discuss potential applications of the numerical method and the effective theory in a range of more general contexts.