Two temperature Ising Model

We introduce a two-temperature Ising model as a prototype of superstatistic critical phenomena. The model is described by two temperatures (\(T_1,T_2\)) in zero magnetic field. To predict the phase diagram and numerically estimate the exponents, we develop Metropolis and Swendsen-Wang Monte Carlo method. We observe that there is a non-trivial critical line, separating ordered and disordered phases. We propose an analytic equation for the critical line in the phase diagram. Our numerical estimation of the critical exponents illustrates that all points on the critical line belong to the ordinary Ising universality class.