Abstract
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 not a 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.
Highlights
Nonequilibrium relaxation processes have been extensively studied during the last decades
The most technical parts of our work are explained in two Appendixes: In Appendix A we show how we have implemented the Monte Carlo (MC) dynamics, and Published by the American Physical Society
It is well known that in the ferromagnetic phase, and excluding fast initial relaxations, E (t ) and ξ (t ) are tightly connected [12]: (E (t ) − Eeq) ∝ 1/ξ (t ), because the excess energy is located at the boundaries of the magnetic domains. This is the behavior found for κ > κc: see Fig. 3(a) and the lower three curves in the inset of that figure. We find that this strong connection extends to the paramagnetic phase where, close to the equilibrium, the magnetic domains grow without changing the system energy [see the top two curves displayed in the inset of Fig. 3(a)]
Summary
Nonequilibrium relaxation processes have been extensively studied during the last decades. We understand which are the general conditions allowing for faster coolings, or faster heatings, in Markovian systems [3,4], granular matter [5,6], spin glasses [7], water [8], the quantum Ising spin model [9], and very recently the generalization to Markovian open quantum systems [10] On these grounds, Amit and Raz have designed a novel strategy, useful in systems with timescale separation, in which precooling the system results in a faster heating [11]. In Appendix B we explain how to perform the spatial integrals of the two-point correlation function
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