Kinetics of the two-dimensional long-range Ising model at low temperatures

We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling J(r) similar to r(-(d+sigma)), where d = 2 is the dimensionality. According to the Bray-Rutenberg predictions, the exponent sigma controls the algebraic growth in time of the characteristic domain size L(t), L(t) similar to t(1/z), with growth exponent z = 1 + sigma for sigma < 1 and z = 2 for sigma > 1. These results hold for quenches to a nonzero temperature T > 0 below the critical temperature T-c. We show that, in the case of quenches to T = 0, due to the long-range interactions, the interfaces experience a drift which makes the dynamics of the system peculiar. More precisely, we find that in this case the growth exponent takes the value z = 4/3, independently of sigma, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for single domains.