Kinetics of true mean-field Ising models and the Langevin equation: A comparison

Abstract

We compare the exact kinetics of the Langevin equation and two kinetic Ising models for the case of true mean-field interactions. Kinetic Ising model I is the traditional Monte Carlo approach-spins are picked at random and flipped according to a heat-bath probabiilty function. In analogy to diffusive mechanisms in crystals, model II incorporates a large energy barrier to motion and the spin-flip rate is exponentially activated. The behaviors of these two spin-flip models are in general fundamentally different. The model-I kinetics saturate with increasing driving enthalpy while the model-II kinetics do not. If the Langevin kinetic coefficient Γ is taken to be constant, agreement between the Langevin and spin-flip kinetics is limited to the linear-response regime. However, if Γ is allowed to vary with the instantaneous magnetization, good agreement extends to the intermediate-driving-force regime scrF∼0.5kBT. For large driving forces scrFkBT, the Langevin kinetics is intrinsically different from that of either spin model. © 1992 The American Physical Society.