# Competitive nucleation and the Ostwald rule in a generalized Potts model with multiple metastable phases

## TL;DR

This paper presents a spin model with multiple metastable phases to study nucleation pathways, revealing that the Ostwald rule requires probabilistic modification when phases are similarly stable and that nucleation rates depend on accessible phases.

## Contribution

It introduces a generalized Potts model with controllable metastable phases and a method to extract individual nucleation rates from simulations, advancing understanding of competitive nucleation.

## Key findings

- Nucleation pathways can involve arbitrarily long metastable sequences.
- The Ostwald rule is probabilistically modified when phases are nearly equally stable.
- Nucleation rates depend on the number of accessible phases.

## Abstract

We introduce a simple nearest-neighbor spin model with multiple metastable phases, the number and decay pathways of which are explicitly controlled by the parameters of the system. With this model we can construct, for example, a system which evolves through an arbitrarily long succession of metastable phases. We also construct systems in which different phases may nucleate competitively from a single initial phase. For such a system, we present a general method to extract from numerical simulations the individual nucleation rates of the nucleating phases. The results show that the Ostwald rule, which predicts which phase will nucleate, must be modified probabilistically when the new phases are almost equally stable. Finally, we show that the nucleation rate of a phase depends, among other things, on the number of other phases accessible from it.