jstatJSMTC6Journal of Statistical Mechanics: Theory and ExperimentJSTATJ. Stat. Mech.1742-5468IOP Publishing and SISSAjstatac289510.1088/1742-5468/ac2895ac2895JSTAT_043P_0721PaperPAPER: Classical statistical mechanics, equilibrium and non-equilibriumDynamical phase transition in the activity-biased fully-connected random field Ising model: connection with glass-forming systemsGuiothJules1rlj22@cam.ac.uk2JackRobert L13* Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom Univ. Lyon, ÉNS de Lyon, Univ. Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom

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1020212010202120102021202110103206307202112920212192021© 2021 The Author(s). Published on behalf of SISSA Medialab srl by IOP Publishing Ltd2021 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.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.

kinetic Ising modelslarge deviations in non-equilibrium systemsslow relaxation, glassy dynamics, ageingccc1742-5468/21/103206+30$33.00printedPrinted in the UKcrossmarkyes