Slow quench dynamics of the Baxter-Wu model

Using Monte Carlo simulations, we investigate the dynamical properties of the Baxter-Wu model under slow quenches, i.e., tuning the temperature slowly. For the cooling process, the scaling behavior of the excess defect density in the critical region aligns well with the predictions of the Kibble-Zurek (KZ) mechanism. However, the scaling behavior of the excess defect density after exiting the impulse regime does not follow from a simple interplay between the KZ mechanism and the coarsening dynamics; the system undergoes a decay close to a power-law form with an exponent that is significantly different from the coarsening exponent observed in instantaneous quenching. For the heating process, we show that if the system starts from its ground state, the relevant exponents describing the KZ mechanism are identical to those in the cooling scenario. Furthermore, in the heating process, we find that the system does not directly enter the adiabatic regime after leaving the impulse regime but instead passes through a crossover regime with an exponential decay of the excess defect density. If the initial state is ordered but not the ground state of the system, the defect density exhibits a good scaling behavior, but the relevant exponents do not conform to the predictions of the KZ mechanism.