Nucleation in a sheared Ising model: effects of external field

TL;DR

This study investigates how external magnetic fields influence nucleation rates and cluster properties in a sheared 2D Ising model, revealing nonmonotonic behaviors and limitations of classical nucleation theory under shear conditions.

Contribution

It extends understanding of nucleation under shear by analyzing external field effects and comparing results to classical nucleation theory, highlighting its limitations.

Findings

Nucleation rate exhibits nonmonotonic dependence on shear rate.

Peak nucleation rate is insensitive to external field at low field strengths.

Transition state clusters become larger and more elongated as the external field decreases.

Abstract

Simulations using the Forward Flux Sampling method have shown a nonmonotonic de- pendence of the homogeneous nucleation rate on the shear rate for a sheared two dimensional Ising model [R. J. Allen et al, arXiv cond-mat/0805.3029]. For quasi-equilibrium systems (i.e. in the absence of shear), Classical Nucleation Theory (CNT) predicts the dependence of the critical cluster size and the nucleation rate on the external magnetic field. We investigate the behaviour of the sheared Ising model as a function of the external field. At low exter- nal field strength, the same nonmonotonic behaviour holds and the peak in the nucleation rate is remarkably insensitive to the field strength. This suggests that the same external field-dependence holds for the enhancement of nucleation by shear at low shear rates and the suppression of shear at high shear rates. At high field strength, the nucleation behaviour is qualitatively different. We also analyse the size and shape of the largest cluster in the transition state configurations, as a function of the external field. In the sheared system, the transition state cluster becomes larger and more elongated as the field strength decreases. We compare our results for the sheared system to the predictions of the CNT for the quasi- equilibrium case, and find that the CNT cannot easily be used to describe nucleation in the system under shear.