Nucleation for one-dimensional long-range Ising models

TL;DR

This paper investigates metastability in one-dimensional long-range Ising models, identifying the unique metastable state, estimating transition times, and illustrating how the critical droplet size varies with external magnetic field.

Contribution

It provides a general theoretical framework for metastability in long-range 1D Ising models and demonstrates the nature of critical droplets in different interaction regimes.

Findings

- Configuration -1 is the unique metastable state.

- Mean exit time is estimated.

- Critical droplet size varies with magnetic field.

Abstract

In this note we study metastability phenomena for a class of long-range Ising models in one-dimension. We prove that, under suitable general conditions, the configuration -1 is the only metastable state and we estimate the mean exit time. Moreover, we illustrate the theory with two examples (exponentially and polynomially decaying interaction) and we show that the critical droplet can be macroscopic or mesoscopic, according to the value of the external magnetic field.