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تسجيل مستخدم جديدZero-Temperature Coarsening in the Two-Dimensional Long-Range Ising Model
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We investigate the nonequilibrium dynamics following a quench to zero temperature of the non-conserved Ising model with power-law decaying long-range interactions $propto 1/r^{d+sigma}$ 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 $alpha$, the persistence exponent $theta$, and the fractal dimension $d_f$. It is found that the growth exponent $alphaapprox 3/4$ is independent of $sigma$ and different from $alpha=1/2$ as expected for nearest-neighbor models. In the large $sigma$ 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 $theta$ this is a direct consequence of the different growth exponents $alpha$ as can be understood from the relation $d-d_f=theta/alpha$; 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 $sigma$ studied, reinforcing its general validity.
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