Particle transport based study of nucleation in a ferromagnetic three-state spin system with conservative dynamics

TL;DR

This paper investigates metastability in a three-state ferromagnetic spin system with conservative dynamics, introducing a new spin transport approach to analyze transition times and configurations.

Contribution

It develops a novel spin transport method applicable to multi-state spin models, providing detailed metastability analysis for the Blume--Capel model with Kawasaki dynamics.

Findings

Identifies the unique metastable state as the homogeneous minus state.

Estimates the exit time from the metastable state.

Introduces a new spin transport approach for complex configuration analysis.

Abstract

We pose the problem of metastability for a three--state spin system with conservative dynamics. We consider the Blume--Capel model with the Kawasaki dynamics, we prove that, in a particular region of the parameter plane, the metastable state is the unique homogeneous minus state, and we estimate the exit time. To achieve our goal we have to solve several variational problems in the configuration space which result to be particularly involved, due to complicated structure of the trajectories. They key ingredient is the control of the energy differences between the configurations crossed when a spin is transported from the boundary to an internal site of the lattice through a completely arbitrary mixture of the three--state spin species. To master these mechanisms we have introduced a new approach based on the transport of spins along nearest neighbor connected regions of the lattice with constant spin configuration. This novel approach goes beyond the Blume--Capel model and can be used for the study of more general multi--state spin models.