Ising model with stochastic resetting

  title={Ising model with stochastic resetting},
  author={Matteo Magoni and Satya N. Majumdar and Gr{\'e}gory Schehr},
  journal={arXiv: Statistical Mechanics},
We study the stationary properties of the Ising model that, while evolving towards its equilibrium state at temperature $T$ according to the Glauber dynamics, is stochastically reset to its fixed initial configuration with magnetisation $m_0$ at a constant rate $r$. Resetting breaks detailed balance and drives the system to a non-equilibrium stationary state where the magnetisation acquires a nontrivial distribution, leading to a rich phase diagram in the $(T,r)$ plane. We establish these… 

Figures from this paper

Nonanalytic nonequilibrium field theory: Stochastic reheating of the Ising model

Many-body non-equilibrium steady states can still be described by a Landau-Ginzburg theory if one allows non-analytic terms in the potential. We substantiate this claim by working out the case of the

Renewal processes with a trap under stochastic resetting

Renewal processes are zero-dimensional processes defined by independent intervals of time between zero crossings or a random walker. The distribution of the occupation times of the sign states are

Discrete space-time resetting model: application to first-passage and transmission statistics

We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability

Voter model under stochastic resetting

The voter model is a toy model of consensus formation based on nearest-neighbour inter-actions. Each voter is endowed with a Boolean variable (a binary opinion) that flips randomly at a rate set

Biased random walk on random networks in presence of stochastic resetting: exact results

We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the

Conditioned backward and forward times of diffusion with stochastic resetting: A renewal theory approach.

Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion

An advection-diffusion process with proportional resetting

This paper presents a diffusion process with a novel resetting mechanism in which the amplitude of the process is instantaneously converted to a proportion of its value at random times. This model is

Restoring ergodicity of stochastically reset anomalous-diffusion processes

Wei Wang ,1,2,* Andrey G. Cherstvy ,2,3,† Ralf Metzler ,2,‡ and Igor M. Sokolov 3,4,§ 1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany 2Institute

Synchronization in the Kuramoto model in presence of stochastic resetting.

What happens when the paradigmatic Kuramoto model involving interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is




  • 4, 294
  • 1963

Totally asymmetric simple exclusion process with resetting

We study the one-dimensional totally asymmetric simple exclusion process (TASEP) with open boundaries having the additional dynamical feature of stochastic resetting to the initial, empty state. The

Stochastic resetting and applications

In this topical review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose

Non-conserving zero-range processes with extensive rates under resetting

We consider a non-conserving zero-range process with hopping rate proportional to the number of particles at each site. Particles are added to the system with a site-dependent creation rate, and

Work Fluctuations and Jarzynski Equality in Stochastic Resetting.

It is shown that the distribution function of the work typically, in asymptotic times, converges to a universal Gaussian form for any protocol as long as that is also renewed after each resetting event.

Invariants of motion with stochastic resetting and space-time coupled returns

Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time

Time-dependent density of diffusion with stochastic resetting is invariant to return speed.

A situation where upon resetting the diffusing particle returns to the origin at a finite (rather than infinite) speed is considered, and the time-dependent distribution describing the particle's position in this model is completely invariant to the speed of return.

Symmetric exclusion process under stochastic resetting.

While the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behavior.

Landau-like expansion for phase transitions in stochastic resetting

A Landau like theory is developed to characterize the phase transitions in resetting systems and it is shown how the transition can be understood by analyzing the first passage time moments.

The interplay between population genetics and diffusion with stochastic resetting

This article obtains the mean first-passage time for the Ohta–Kimura continuous ladder model and establishes the correlation between particles in the stochastic resetting model, and studies the non-equilibrium stationary distribution for two interacting resetting particles.