Critical fluctuations of time-dependent magnetization in a random-field Ising model

Cooperative behaviors near the disorder-induced critical point in a random field Ising model are numerically investigated by analyzing time-dependent magnetization in ordering processes from a special initial condition. We find that the intensity of fluctuations of time-dependent magnetization, $\chi(t)$, attains a maximum value at a time $t=\tau$ in a normal phase and that $\chi(\tau)$ and $\tau$ exhibit divergences near the disorder-induced critical point. Furthermore, spin configurations around the time $\tau$ are characterized by a length scale, which also exhibits a divergence near the critical point. We estimate the critical exponents that characterize these power-law divergences by using a finite-size scaling method.