title: Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model.
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 multicanonical 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.
authors.affiliation: Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Paris Cité, UMR 7599 CNRS, Université Paris Diderot, 75013 Paris, France.|Philippe Meyer Institute for Theoretical Physics, Physics Department, École Normale Supérieure & PSL Research University, 24 rue Lhomond, 75231 Paris Cedex 05, France.
authors.forename: Takahiro
authors.initials: T
authors.lastname: Nemoto
authors.affiliation: Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom.
authors.forename: Robert L
authors.initials: RL
authors.lastname: Jack
authors.affiliation: Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Paris Cité, UMR 7599 CNRS, Université Paris Diderot, 75013 Paris, France.|LIPhy, Université Grenoble Alpes and CNRS, F-38042 Grenoble, France.
authors.forename: Vivien
authors.initials: V
authors.lastname: Lecomte