Critical Slowing Down Along the Dynamic Phase Boundary in Ising Meanfield Dynamics

TL;DR

This paper investigates the critical slowing down in the dynamic phase transition of meanfield Ising ferromagnets under oscillating magnetic fields, analyzing relaxation times and their divergence near the transition boundary.

Contribution

It introduces a detailed analysis of relaxation behavior and critical slowing down in meanfield Ising models, including power law divergence and exponent estimation.

Findings

Critical slowing down observed along the dynamic phase boundary.

Power law divergence of relaxation time near transition.

Dependence of relaxation dynamics on magnetic field amplitude.

Abstract

We studied the dynamical phase transition in kinetic Ising ferromagnets driven by oscillating magnetic field in meanfield approximation. The meanfield differential equation was solved by sixth order Runge-Kutta-Felberg method. The time averaged magnetisation plays the role of the dynamic order parameter. We studied the relaxation behaviour of the dynamic order parameter close to the transition temperature, which depends on the amplitude of the applied magnetic field. We observed the critical slowing down along the dynamic phase boundary. We proposed a power law divergence of the relaxation time and estimated the exponent. We also found its dependence on the field amplitude and compared the result with the exact value in limiting case.