Length and time scale divergences at the magnetization-reversal transition in the Ising model

TL;DR

This paper investigates the divergence of length and time scales at the magnetization-reversal transition in the Ising model, combining mean field theory, Monte Carlo simulations, and nucleation theory to analyze critical behavior.

Contribution

It provides a detailed analysis of scale divergences at the transition, comparing mean field predictions with simulation results and offering a qualitative explanation via nucleation theory.

Findings

Both length and time scales diverge at the transition point.

Mean field and Monte Carlo results show similar but not identical growth patterns.

Nucleation theory qualitatively explains the nature of the time scale divergence.

Abstract

The divergences of both the length and time scales, at the magnetization- reversal transition in Ising model under a pulsed field, have been studied in the linearized limit of the mean field theory. Both length and time scales are shown to diverge at the transition point and it has been checked that the nature of the time scale divergence agrees well with the result obtained from the numerical solution of the mean field equation of motion. Similar growths in length and time scales are also observed, as one approaches the transition point, using Monte Carlo simulations. However, these are not of the same nature as the mean field case. Nucleation theory provides a qualitative argument which explains the nature of the time scale growth. To study the nature of growth of the characteristic length scale, we have looked at the cluster size distribution of the reversed spin domains and defined a pseudo-correlation length which has been observed to grow at the phase boundary of the transition.