Nucleation rate in the two dimensional Ising model in the presence of random impurities

TL;DR

This study investigates how static and dynamic impurities affect nucleation in the two-dimensional Ising model, revealing that impurities lower the free energy barrier and critical nucleus size, thus enhancing nucleation rates.

Contribution

It provides the first detailed analysis of impurity effects on nucleation in the 2D Ising model, comparing static and dynamic impurities and validating nucleation rate calculations with classical theory and simulations.

Findings

Impurity density reduces free energy barrier and critical nucleus size.

Nucleation rates increase with impurity density, matching classical theory.

Dynamic impurities tend to occupy nucleus boundaries at low temperatures.

Abstract

Nucleation phenomena are ubiquitous in nature and the presence of impurities in every real and experimental system is unavoidable. Yet numerical studies of nucleation are nearly always conducted for entirely pure systems. We have studied the behaviour of the droplet free energy in two dimensional Ising model in the presence of randomly positioned static and dynamic impurities. We have shown that both the free energy barrier height and critical nucleus size monotonically decreases with increasing the impurity density for the static case. We have compared the nucleation rates obtained from Classical Nucleation Theory and the Forward Flux Sampling method for different densities of the static impurities. The results show good agreement. In the case of dynamic impurities, we observe preferential occupancy the impurities at the boundary positions of the nucleus when the temperature is low. This further boosts enhancement of the nucleation rate due to lowering of the effective interfacial free energy.