Low temperature nucleation rate calculations using the N-Fold way

TL;DR

This paper introduces an efficient numerical approach using the N-Fold way algorithm to calculate extremely low nucleation rates in the Ising model at low temperatures, including effects of impurities.

Contribution

It presents a novel combination of the N-Fold way with a new cluster identification algorithm to access unprecedentedly low nucleation rates in the Ising model.

Findings

Classical nucleation theory applies across studied temperature ranges.

Static impurities do not significantly alter nucleation rates.

Mobile impurities reduce the effectiveness of umbrella sampling at low mobility.

Abstract

We present a numerical study to determine nucleation rates for magnetisation reversal within the Ising model (lattice gas model) in the low-temperature regime, a domain less explored in previous research. To achieve this, we implemented the N-Fold way algorithm, a well-established method for low-temperature simulations, alongside a novel, highly efficient cluster identification algorithm. Our method can access nucleation rates up to 50 orders of magnitude lower than previously reported results. We examine three cases: homogeneous pure system, system with static impurities, and system with mobile impurities, where impurities are defined as sites with zero interactions with neighbouring spins (spin value of impurities is set to 0). Classical nucleation theory holds across the entire temperature range studied in the paper, for both the homogeneous system and the static impurity case. However, in the case of mobile impurities, the umbrella sampling technique seems ineffective at low mobility values. These findings provide valuable insights into nucleation phenomena at low temperatures, contributing to theoretical and experimental understanding.