Coarsening in the long-range Ising model with conserved dynamics

While the kinetics of domain growth, even for conserved order-parameter dynamics, is widely studied for short-range inter-particle interactions, systems having long-range interactions are receiving attention only recently. Here, we present results, for such dynamics, from a Monte Carlo (MC) study of the two-dimensional long-range Ising model, with focus on critical compositions of up and down spins. The order parameter in the MC simulations was conserved via the incorporation of the Kawasaki spin-exchange method. The simulation results for domain growth, following quenches of the homogeneous systems to temperatures below the critical values \(T_c\), were analyzed via a method analogous to the finite-size scaling technique of equilibrium critical phenomena and other advanced methods. The outcomes reveal that the growths follow power laws, with the exponent having interesting dependence on the range of interaction. Quite interestingly, when the range is above a cut-off, the exponent, for any given range, seems to change from a larger value to a smaller one, during the evolution process. While the corresponding values at late times match with certain theoretical predictions for the conserved order-parameter dynamics, the ones at the early times appear surprisingly high, often quite close to even the theoretical values for the nonconserved case.