Dynamics of Baxter-Wu model

TL;DR

This study uses Monte Carlo simulations to explore the dynamical behavior of the Baxter-Wu model during linear temperature quenches, revealing complex scaling behaviors and deviations from the Kibble-Zurek mechanism in certain regimes.

Contribution

It provides new insights into the dynamical scaling and defect decay processes of the Baxter-Wu model under linear quenches, highlighting deviations from existing theories.

Findings

Scaling of excess defect density aligns with KZ predictions during cooling.

Post-impulse regime decay follows a power-law with a different exponent.

Crossover regime exhibits exponential decay of defect density after leaving the impulse regime.

Abstract

Using Monte Carlo simulations, we investigate the dynamical properties of the Baxter-Wu (BW) model under linear quenches. For the linear 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 linear 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. 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.