Response of the two-dimensional kinetic Ising model under a stochastic field

Abstract

We study, using Monte Carlo dynamics, the time (t) dependent average magnetization per spin m(t) behavior of the 2D kinetic Ising model under a binary (±h0) stochastic field h(t). The time dependence of the stochastic field is such that its average over each successive time interval τ is assured to be zero (without any fluctuation). The average magnetization $Q=(1/\tau )\int \nolimits _{0}^{\tau }m(t)\hspace{0.167em} \mathrm{d}t$ is considered as an order parameter of the system. The phase diagram in (h0,τ) plane is obtained. Fluctuations in the 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 h0 below some threshold value ${h}_{0}^{\mathrm{c}}(\tau )$ (dependent on τ values; ${h}_{0}^{\mathrm{c}}\rightarrow 0$ as τ → ∞ across the phase boundary). Beyond these ${h}_{0}^{\mathrm{c}}(\tau )$, the transition is no longer continuous.