Stochastic two-temperature nonequilibrium Ising model

Abstract We investigate the nonequilibrium stationary state (NESS) of the two-dimensional Ising model under a stochastic dichotomous modulation of temperature, which alternates between T c ± δ around the critical temperature T c at a rate γ . Both magnetisation and energy exhibit non-monotonic dependence on γ , explained by a renewal approach in the slow-switching limit, while for small δ dynamical response theory quantitatively captures the γ -dependence of the observables. In the fast-switching regime, the NESS appears Boltzmann-like with a γ -dependent effective temperature. However, a finite energy current flowing through the system from hot to cold reservoir confirms the intrinsic nonequilibrium nature of the dynamics.