Response of Two-dimensional Kinetic Ising Model under Stochastic Field

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.