Dynamical off-equilibrium scaling across magnetic first-order phase transitions
Résumé
We investigate the off-equilibrium dynamics of a classical spin system with symmetry in 2 < D < 4 spatial dimensions and in the limit . The system is set up in an ordered equilibrium state and is subsequently driven out of equilibrium by slowly varying the external magnetic field h across the transition line at fixed temperature . We distinguish the cases where the magnetic transition is continuous and 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.