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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>c</mml:mtext> </mml:msub> <mml:mo>±</mml:mo> <mml:mi>δ</mml:mi> </mml:mrow> </mml:math> around the critical temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>c</mml:mtext> </mml:msub> </mml:mrow> </mml:math> 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.