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 <Subscript>1</Subscript> > T <Subscript> c </Subscript> > T <Subscript>2</Subscript>, where T <Subscript> c </Subscript> is the Onsager critical temperature. In this way one can observe a phase transition between an ordered phase (T > T <Subscript> c </Subscript>) and a disordered one (T > T <Subscript> c </Subscript>) 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 <Subscript>0</Subscript>, 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. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012