Ising Model with Power Law Resetting

TL;DR

This paper explores how power law stochastic resetting affects the nonequilibrium dynamics of the Ising model, revealing new phases and behaviors not seen with exponential resetting, supported by analytical and simulation results.

Contribution

It introduces the study of Ising model dynamics under power law resetting, uncovering novel phase transitions and nonequilibrium states distinct from exponential resetting cases.

Findings

Power law resetting leads to non-trivial magnetisation distributions.

No steady state exists for $oldsymbol{ extit{ extalpha}} < 1$, but a stationary state appears for $ extalpha > 1$.

Distinct ferromagnetic phases emerge depending on the exponent $ extalpha$ and temperature.

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.