Ising model with stochastic resetting

Abstract

We study the nonequilibrium stationary state (NESS) of the Ising model driven away from thermal equilibrium at temperature T by a stochastic resetting protocol. This protocol, realizable via rapid quench of temperature and magnetic field, resets the magnetization to its fixed initial value m_{0} at a constant rate r. In the resulting NESS, the magnetization acquires a nontrivial distribution, leading to a rich phase diagram in the (T,r) plane. We establish these results exactly in one dimension and present scaling arguments supported by simulations in two dimensions. We show that this resetting protocol gives rise to a “pseudoferro” phase in the (T,r) plane for r>r^{*}(T) and T>T_{c}, where r^{*}(T) is a crossover line separating the pseudoferro phase from a paramagnetic phase. This pseudoferro phase is characterized by a magnetization distribution that vanishes as ∼m^{ζ} as m→0, where ζ varies continuously with T and r.