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 $T_c\pm \hat{I}´$ around the critical temperature $T_c$ at a rate ${\hat{I}}^3$. Both magnetization and energy exhibit non-monotonic dependence on ${\hat{I}}^3$, explained by a renewal approach in the slow-switching limit, while for small $\hat{I}´$ dynamical response theory quantitatively captures the ${\hat{I}}^3$-dependence of the observables. In the fast-switching regime, the NESS appears Boltzmann-like with a ${\hat{I}}^3$-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.

20 pages, 11 figures; comments and suggestions are welcome