Ising model with stochastic resetting
Abstract
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 m0 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 results exactly in one-dimension and present scaling arguments supported by numerical simulations in two-dimensions. We show that resetting gives rise to a novel "pseudo-ferro" phase in the (T,r) plane for r > r*(T) and T>Tc where r*(T) is a crossover line separating the pseudo-ferro phase from a paramagnetic phase. This pseudo-ferro phase is characterised by a non-zero typical magnetisation and a vanishing gap near m=0 of the magnetisation distribution.