Dynamic Magnetization-Reversal Transition in the Ising Model

TL;DR

This paper investigates the dynamic magnetization-reversal transition in the Ising model through mean field and Monte Carlo methods, revealing phase boundary behavior, critical exponents, and divergence of relaxation times.

Contribution

It provides a combined mean field and Monte Carlo analysis of the dynamic transition, deriving analytical phase boundary expressions and estimating critical exponents.

Findings

Transition occurs below static T_c with external field pulse

Order parameter varies continuously near transition

Relaxation time diverges logarithmically or exponentially

Abstract

We report the results of mean field and the Monte Carlo study of the dynamic magnetization-reversal transition in the Ising model, brought about by the application of an external field pulse applied in opposition to the existing order before the application of the pulse. The transition occurs at a temperature T below the static critical temperature T_c without any external field. The transition occurs when the system, perturbed by the external field pulse competing with the existing order, jumps from one minimum of free energy to the other after the withdrawal of the pulse. The parameters controlling the transition are the strength h_p and the duration Delta t of the pulse. In the mean field case, approximate analytical expression is obtained for the phase boundary which agrees well with that obtained numerically in the small Delta t and large T limit. The order parameter of the transition has been identified and is observed to vary continuously near the transition. The order parameter exponent beta was estimated both for the mean field (beta =1) and the Monte Carlo beta = 0.90 \pm 0.02 in two dimension) cases. The transition shows a "critical slowing-down" type behaviour near the phase boundary with diverging relaxation time. The divergence was found to be logarithmic in the mean field case and exponential in the Monte Carlo case. The finite size scaling technique was employed to estimate the correlation length exponent nu (= 1.5 \pm 0.3 in two dimension) in the Monte Carlo case.