Dynamic off-equilibrium transition in systems slowly driven across thermal first-order phase transitions

We study the off-equilibrium behavior of systems with short-range interactions driven across a thermal first-order transition, where the dynamics is exponentially slow. We consider a dynamics that starts in the high-T phase at time t = t_i<0 and ends in in the low-T phase at t=t_f>0, with a time-dependent temperature T(t)/T_c \approx 1 - t/t_s, where t_s is the protocol time scale. A general off-equilibrium scaling (OS) behavior emerges in the limit of large t_s. We check it at the first-order transition of the two-dimensional q-state Potts model with q=10 and 20. The numerical results show evidence of a dynamic transition, where the OS functions show a spinodal-like singularity. Therefore, the general mean-field picture valid for systems with long-range interactions is qualitatively recovered, provided the time dependence is appropriately (logarithmically) rescaled.