A d dimensional nucleation and growth model

TL;DR

This paper investigates the relaxation time in a generalized ferromagnetic d-dimensional growth model on a lattice, extending previous models by incorporating multiple activation energies based on neighboring occupied sites.

Contribution

It introduces a multi-parameter growth model generalizing prior work, analyzing how activation energies influence relaxation dynamics in higher dimensions.

Findings

Derived bounds for relaxation times in the model

Extended understanding of nucleation and growth processes in higher dimensions

Generalized activation energy effects in ferromagnetic lattice models

Abstract

We analyze the relaxation time of a ferromagnetic d dimensional growth model on the lattice. The model is characterized by d param- eters which represent the activation energies of a site, depending on the number of occupied nearest neighbours. This model is a natural generalisation of the model studied by Dehghanpour and Schonmann [DS97a], where the activation energy of a site with more than two occupied neighbours is zero.