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Recent works unraveled an intriguing finite-time dynamical phase transitionin the thermal relaxation of the mean field Curie-Weiss model. The phasetransition reflects a sudden switch in the dynamics. Its existence in systemswith a finite range of interaction, however, remained unclear. Here wedemonstrate the dynamical phase transition for nearest-neighbor Ising systemson the square and Bethe lattices through extensive computer simulations and byanalytical results. Combining large-deviation techniques and Bethe-Guggenheimtheory we prove the existence of the dynamical phase transition for arbitraryquenches, including those within the two-phase region. Strikingly, for anygiven initial condition we prove and explain the existence of non-trivial speedlimits for the dynamical phase transition and the relaxation of magnetization,which are fully corroborated by simulations of the microscopic Ising model butare absent in the mean field setting. Pair correlations, which are neglected inmean field theory and trivial in the Curie-Weiss model, account for kineticconstraints due to frustrated local configurations that give rise to a globalspeed limit.

Global Speed Limit for Finite-Time Dynamical Phase Transition and Nonequilibrium Relaxation