Dynamical and stationary critical behavior of the Ising ferromagnet in a thermal gradient

In this paper we present and discuss results of Monte Carlo numerical simulations of the two-dimensional Ising ferromagnet in contact with a heat bath that intrinsically has a thermal gradient. The extremes of the magnet are at temperatures T 1 < T c < T 2 , where T c is the Onsager critical temperature. In this way one can observe a phase transition between an ordered phase ( T < T c ) and a disordered one ( T > T c ) by means of a single simulation. By starting the simulations with fully disordered initial configurations with magnetization m ≡ 0 corresponding to T = ∞, which are then suddenly annealed to a preset thermal gradient, we study the short-time critical dynamic behavior of the system. Also, by setting a small initial magnetization m = m 0 , we study the critical initial increase of the order parameter. Furthermore, by starting the simulations from fully ordered configurations, which correspond to the ground state at T = 0 and are subsequently quenched to a preset gradient, we study the critical relaxation dynamics of the system. Additionally, we perform stationary measurements ( t → ∞) that are discussed in terms of the standard finite-size scaling theory. We conclude that our numerical simulation results of the Ising magnet in a thermal gradient, which are rationalized in terms of both dynamic and standard scaling arguments, are fully consistent with well established results obtained under equilibrium conditions.