Slow growth of magnetic domains helps fast evolution routes for out-of-equilibrium dynamics

Cooling and heating faster a system is a crucial problem in science, technology, and industry. Indeed, choosing the best thermal protocol to reach a desired temperature or energy is nota trivial task. Noticeably, we find that the phase transitions may speed up thermalization in systems where there are no conserved quantities. In particular, we show that the slow growth of magnetic domains shortens the overall time that the system takes to reach a final desired state. To prove that statement, we use intensive numerical simulations of a prototypical many-body system, namely, the two-dimensional Ising model.