Kinetics of the two-dimensional long-range Ising model at low temperatures
Ramgopal Agrawal, Federico Corberi, Eugenio Lippiello, Paolo Politi, Sanjay Puri
Abstract
We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling $J(r)\ensuremath{\sim}{r}^{\ensuremath{-}(d+\ensuremath{\sigma})}$, where $d=2$ is the dimensionality. According to the Bray-Rutenberg predictions, the exponent $\ensuremath{\sigma}$ controls the algebraic growth in time of the characteristic domain size $L(t), L(t)\ensuremath{\sim}{t}^{1/z}$, with growth exponent $z=1+\ensuremath{\sigma}$ for $\ensuremath{\sigma}<1$ and $z=2$ for $\ensuremath{\sigma}>1$. 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 $\ensuremath{\sigma}$, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for single domains.