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

摘要

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→∞. 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 h_c = 0 at fixed temperature T≤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.