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

Abstract

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