Nonequilibrium Phase Transition in the Kinetic Ising model: Critical Slowing Down and Specific-heat Singularity

TL;DR

This paper investigates the nonequilibrium phase transition in the kinetic Ising model under oscillating magnetic fields, revealing critical slowing down and specific-heat divergence through simulations and mean field analysis.

Contribution

It demonstrates the divergence of relaxation time and specific heat near the dynamic transition, combining Monte Carlo simulations with mean field solutions.

Findings

Relaxation time diverges near the transition point.

Specific heat exhibits divergence at the transition.

Debye relaxation behavior observed in the dynamic order parameter.

Abstract

The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation and by solving numerically the mean field dynamic equation of motion for the average magnetisation. In both the cases, the Debye 'relaxation' behaviour of the dynamic order parameter has been observed and the 'relaxation time' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean field dynamic equation. The temperature variation of appropiately defined 'specific-heat' is studied by Monte Carlo simulation near the transition point. The specific-heat has been observed to diverge near the dynamic transition point.