Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers

TL;DR

This study compares low-temperature nucleation rates in kinetic Ising models under two Arrhenius dynamics with local energy barriers, revealing significant differences from each other and from Glauber dynamics, emphasizing careful rate design.

Contribution

The paper provides a comparative analysis of two Arrhenius dynamics with local energy barriers in kinetic Ising models, highlighting their differences from Glauber dynamics.

Findings

Different nucleation rates observed with the two dynamics.

Significant deviations from Glauber dynamics.

Implications for designing kinetic Monte Carlo rates.

Abstract

Using both analytical and simulational methods, we study low-temperature nucleation rates in kinetic Ising lattice-gas models that evolve under two different Arrhenius dynamics that interpose between the Ising states a transition state representing a local energy barrier. The two dynamics are the transition-state approximation [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)] and the one-step dynamic [H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989)]. Even though they both obey detailed balance and are here applied to a situation that does not conserve the order parameter, we find significant differences between the nucleation rates observed with the two dynamics, and between them and the standard Glauber dynamic [R. J. Glauber, J. Math. Phys. 4, 294 (1963)], which does not contain transition states. Our results show that great care must be exercised when devising kinetic Monte Carlo transition rates for specific physical or chemical systems.