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

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