学术文献库

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