Crossover from anomalous to normal diffusion: Ising model with stochastic resetting

Abstract

In this paper, we investigate the dynamics of the two-dimensional Ising model with stochastic resetting, utilizing a constant resetting rate procedure with zero-strength initial magnetization. Our results reveal the presence of a characteristic rate r_{c}∼L^{−z}, where L represents the system size and z denotes the dynamical exponent. Below r_{c}, both the equilibrium and dynamical properties remain unchanged. At the same time, for r>r_{c}, the resetting process induces a transition in the probability distribution of the magnetization from a double-peak distribution to a three-peak distribution, ultimately culminating in a single-peak exponential decay. Furthermore, we also find that at the critical points, as r increases, the diffusion of the magnetization changes from anomalous to normal, and the correlation time shifts from being dependent on L to being r-dependent only.