Coarsening in the Long-range Ising Model with Conserved Dynamics

TL;DR

This study investigates domain growth in a two-dimensional long-range Ising model with conserved dynamics, revealing power-law growth with exponents dependent on interaction range and showing different early and late time behaviors.

Contribution

It provides the first Monte Carlo analysis of domain growth in long-range Ising models with conserved order parameters, highlighting the impact of interaction range on growth exponents.

Findings

Growth follows power-laws with exponents depending on interaction range.

Exponents decrease from higher to lower values during evolution when the range exceeds a cutoff.

Early-time exponents are close to nonconserved case predictions, late-time match conserved dynamics theories.

Abstract

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 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 finite-size scaling 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 interstingly, when the range is above a cut-off, the exponent, for any given range, changes 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, quite close to the theoretical values for the nonconserved case.