1. Dynamical phase transition in the activity-biased fully-connected random field Ising model: connection with glass-forming systems
- Author
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Robert L. Jack, Jules Guioth, Apollo - University of Cambridge Repository, and Jack, Robert [0000-0003-0086-4573]
- Subjects
Paper ,Statistics and Probability ,Phase transition ,Field (physics) ,Spontaneous symmetry breaking ,Phase (waves) ,FOS: Physical sciences ,kinetic Ising models ,PAPER: Classical statistical mechanics, equilibrium and non-equilibrium ,01 natural sciences ,010305 fluids & plasmas ,Lattice (order) ,Saddle point ,0103 physical sciences ,Statistical physics ,010306 general physics ,Condensed Matter - Statistical Mechanics ,Physics ,Statistical Mechanics (cond-mat.stat-mech) ,large deviations in non-equilibrium systems ,Statistical and Nonlinear Physics ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,glassy dynamics ,Maxima and minima ,ageing ,slow relaxation ,Ising model ,Statistics, Probability and Uncertainty ,slow relaxation, glassy dynamics, ageing - 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., 26 pages, 10 figures
- Published
- 2021
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