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 ${\alpha }^{\ast }=1-c$: a single-peak ferromagnetic phase localised at $m_{eq}$ for $\alpha <{\alpha }^{\ast }$, and a dual-peak ferromagnetic phase with divergences at $m_{eq}$ and $m_0$ for $\alpha >{\alpha }^{\ast }$. 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.

References in corpus (40)

• Diffusion with Stochastic Resetting
• Unified Scaling Law for Earthquakes
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• First order transition for the optimal search time of Lévy flights with resetting
• Experimental realization of diffusion with stochastic resetting
• Run and tumble particle under resetting: a renewal approach
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Diffusion with resetting in arbitrary spatial dimension
• Stochastic resetting in backtrack recovery by RNA polymerases
• Diffusion with stochastic resetting at power-law times
• Random walks with preferential relocations to places visited in the past and their application to biology
• Fluctuating interfaces subject to stochastic resetting
• First passage under stochastic resetting in an interval
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Boosting search by rare events
• Quantum dynamics with stochastic reset
• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Random walk with random resetting to the maximum
• Symmetric Exclusion Process under Stochastic Resetting
• Effect of Partial Absorption on Diffusion with Resetting
• Diffusion with stochastic resetting is invariant to return speed
• Stochastic resetting with stochastic returns using external trap
• Ising model with stochastic resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Invariants of motion with stochastic resetting and space-time coupled returns
• Sisyphus random walk
• Long time scaling behaviour for diffusion with resetting and memory
• Spectral content of fractional Brownian motion with stochastic reset
• Stochastic resetting in interacting particle systems: A review
• Interacting Brownian Motion with Resetting
• Resetting with stochastic return through linear confining potential
• Diffusion with Resetting Inside a Circle
• Resetting of fluctuating interfaces at power-law times
• Lotka-Volterra systems with stochastic resetting
• Diffusion with Local Resetting and Exclusion
• Modeling long-range memory trading activity by stochastic differential equations
• Zero-current Nonequilibrium State in Symmetric Exclusion Process with Dichotomous Stochastic Resetting
• Stationarity of the inter-event power-law distributions
• Simple Exclusion Processes with Local Resetting