Relaxation behavior near the first-order phase transition line

TL;DR

This study uses simulations to analyze the relaxation dynamics of the 3D kinetic Ising model near the first-order phase transition line, revealing ultra-slow relaxation and complex scaling behaviors across temperatures.

Contribution

It provides new insights into the dynamic scaling and relaxation times near the first-order phase transition in the kinetic Ising model, highlighting behaviors far from criticality.

Findings

Average equilibration time increases significantly at low temperatures.

Ultra-slow relaxation observed along the first-order phase transition line.

Dynamic scaling holds at temperatures much lower than the critical temperature.

Abstract

Using the Metropolis algorithm, we simulate the relaxation process of the three-dimensional kinetic Ising model. Starting from a random initial configuration, we first present the average equilibration time across the entire phase boundary. It is observed that the average equilibration time increases significantly as the temperature decreases far from the critical temperature $T_{\rm c}$. The average equilibration time along the first-order phase transition (1st-PT) line exhibits an ultra-slow relaxation. We also investigate the dynamic scaling behavior with system sizes, and find that dynamic scaling holds not only near $T_{\rm c}$, but also at $T\ll T_{\rm c}$. The dynamic exponent at $T\ll T_{\rm c}$ is larger than that near $T_{\rm c}$. Additionally, we analyze the dynamic scaling of the average autocorrelation time and find that it depends on system size only near $T_{\rm c}$, while it becomes size-independent both above and below $T_{\rm c}$. The extremely slow relaxation dynamics observed near the 1st-PT is attributed to the complex structure of the free energy.