Ising Model with Power Law Resetting

Abstract

We investigate the nonequilibrium dynamics of the nearest-neighbour Ising model subjected to stochastic resetting, where the system is intermittently returned to an initial configuration with magnetisation $m_0$, with the inter-reset times drawn from the power law distribution $\alpha \tau_0^\alpha / \tau^{\alpha+1}$. The heavy-tailed resets generate magnetisation distributions that differ significantly from both equilibrium dynamics and the previously studied Ising model with exponentially distributed reset times. In two dimensions, for $T > T_C$, we find a quasi-ferro state for all $\alpha$, marked by a double-peaked distribution that diverges at $m=0$ and $m=m_0$; no steady state exists for $\alpha < 1$, while a stationary state emerges for $\alpha > 1$. For $T < T_C$, power law resetting produces two distinct regimes separated by a crossover exponent $\alpha^* = 1-c$: a single-peak ferromagnetic phase localised at $m_{eq}$ for $\alpha < \alpha^*$, and a dual-peak ferromagnetic phase with divergences at $m_{eq}$ and $m_0$ for $\alpha > \alpha^*$. Analytic results in one and two dimensions, supported by simulations, yield a rich phase diagram in the $(T,\alpha)$ plane and reveal how heavy-tailed resetting generates nonequilibrium phases very different from those seen in the case of exponential resetting.