Zero-temperature coarsening in the two-dimensional long-range Ising model

We investigate the nonequilibrium dynamics following a quench to zero temperature of nonconserved Ising model with power-law decaying long-range interactions $\ensuremath{\propto}1/{r}^{d+\ensuremath{\sigma}}$ in $d=2$ spatial dimensions. The zero-temperature coarsening is always special interest among processes, because often peculiar behavior observed. provide estimates exponents, viz., growth exponent $\ensuremath{\alpha}$, persistence $\ensuremath{\theta}$, and fractal dimension ${d}_{f}$. It found that $\ensuremath{\alpha}\ensuremath{\approx}3/4$ independent $\ensuremath{\sigma}$ different from $\ensuremath{\alpha}=1/2$, as expected for nearest-neighbor models. In large regime tunable only ${d}_{f}$ recovered, while other exponents differ significantly. For $\ensuremath{\theta}$ this direct consequence $\ensuremath{\alpha}$ can be understood relation $d\ensuremath{-}{d}_{f}=\ensuremath{\theta}/\ensuremath{\alpha}$; they just by ratio $\ensuremath{\approx}3/2$. This has been proposed annihilation processes later numerically tested model. confirm all studied, reinforcing its general validity.