Response of Two-dimensional Kinetic Ising Model under Stochastic Field

TL;DR

This study investigates the dynamic response and phase transition behavior of a 2D kinetic Ising model under a stochastic binary field, revealing Ising-like transitions below a threshold and discontinuous transitions beyond.

Contribution

It introduces a phase diagram in the ($h_0, au$) plane for the 2D kinetic Ising model under stochastic fields and analyzes the nature of phase transitions with respect to field amplitude and time interval.

Findings

Phase diagram in ($h_0, au$) plane established.

Transition is Ising-like below a threshold $h_0^c( au)$.

Transitions become discontinuous beyond $h_0^c( au)$.

Abstract

We study, using Monte Carlo dynamics, the time ($t$) dependent average magnetization per spin $m(t)$ behavior of 2-D kinetic Ising model under a binary ($\pm h_0$) stochastic field $h(t)$. The time dependence of the stochastic field is such that its average over each successive time interval $\tau$ is assured to be zero (without any fluctuation). The average magnetization $Q=(1/\tau)\int_{0}^{\tau} m(t) dt$ is considered as order parameter of the system. The phase diagram in ($h_0,\tau$) plane is obtained. Fluctuations in order parameter and their scaling properties are studied across the phase boundary. These studies indicate that the nature of the transition is Ising like (static Ising universality class) for field amplitudes $h_0$ below some threshold value $h_0^c(\tau)$ (dependent on $\tau$ values; $h_0^c\rightarrow0$ as $\tau\rightarrow\infty$ across the phase boundary) . Beyond these $h_0^c (\tau)$, the transition is no longer continuous.