Metastability and Nucleation for the Blume-Capel Model. Different mechanisms of transition

TL;DR

This paper investigates the metastable behavior and nucleation mechanisms of the Blume-Capel model, revealing an abrupt change in transition dynamics when crossing a specific parameter line at zero temperature.

Contribution

It provides a detailed analysis of transition times and trajectory structures, highlighting a novel abrupt change in transition mechanisms at a critical parameter line.

Findings

Transition time asymptotics computed.

Typical transition trajectories characterized.

Mechanism change occurs at h=2*lambda line.

Abstract

We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbour two-dimensional lattice system with spin variables taking values in -1,0,+1. We consider large but finite volume, small fixed magnetic field h and chemical potential "lambda" in the limit of zero temperature; we analyze the first excursion from the metastable -1 configuration to the stable +1 configuration. We compute the asymptotic behaviour of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the line h=2*lambda is crossed.