Dynamical off-equilibrium scaling across magnetic first-order phase transitions

Abstract

We investigate the off-equilibrium dynamics of a classical spin system with $O(n)$ symmetry in $2<D<4$ spatial dimensions and in the limit $n\to \infty$. The system is set up in an ordered equilibrium state is and subsequently driven out of equilibrium by slowly varying the external magnetic field $h$ across the transition line $h_c=0$ at fixed temperature $T\le T_c$. We distinguish the cases $T=T_c$ where the magnetic transition is continuous and $T<T_c$ where the transition is discontinuous. In the former case, we apply a standard Kibble-Zurek approach to describe the non-equilibrium scaling and formally compute the correlation functions and scaling relations. For the discontinuous transition we develop a scaling theory which builds on the coherence length rather than the correlation length since the latter remains finite for all times. Finally, we derive the off-equilibrium scaling relations for the hysteresis loop area during a round-trip protocol that takes the system across its phase transition and back. Remarkably, our results are valid beyond the large-$n$ limit.

arXiv comment27 pages, 13 figures; accepted in Journal of Statistical Mechanics : Theory and Experiment

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Cited by in corpus (10)

• Coherent and dissipative dynamics at quantum phase transitions
• Out-of-equilibrium scaling behavior arising during round-trip protocols across a quantum first-order transition
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Entanglement in the Quantum Spherical Model -- a Review
• Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models
• Hysteresis in magnets
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• Non-equilibrium dynamics of the open quantum $O(n)$-model with non-Markovian noise: exact results