KINETICS OF TRUE MEAN-FIELD ISING-MODELS AND THE LANGEVIN EQUATION - A COMPARISON

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 probability 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-GAMMA is taken to be constant, agreement between the Langevin and spin-flip kinetics is limited to the linear-response regime. However, if GAMMA is allowed to vary with the instantaneous magnetization, good agreement extends to the intermediate-driving-force regime F is similar to 0.5 k(B)T. For large driving forces F greater than or similar to k(B)T, the Langevin kinetics is intrinsically different from that of either spin model.