Crossover from Anomalous to Normal Diffusion: Ising Model with Stochastic Resetting

TL;DR

This study explores how stochastic resetting affects the diffusion and magnetization distribution in the 2D Ising model, revealing a transition from anomalous to normal diffusion at a critical resetting rate.

Contribution

It introduces the concept of a critical resetting rate in the Ising model, showing how resetting induces a phase transition in magnetization distribution and diffusion behavior.

Findings

Existence of a characteristic resetting rate $r_c$ scaling as $L^{-z}$.

Transition from double-peak to single-peak magnetization distribution with increasing $r$.

Change from anomalous to normal diffusion at the critical point.

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 $r_c \sim L^{-z}$, 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. Besides, 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.