Domain-growth scaling in systems with long-range interactions

The growth kinetics of a system quenched into the ordered phase from high temperatures is considered for systems with power-law interactions of the form 1/${\mathit{r}}^{\mathit{d}+\mathrm{\sigma }}$, with 0<σ1, the characteristic scale L(t), which describes the growth of order at late times, is predicted to obey the conventional Lifshitz-Slyozov and Lifshitz-Cahn-Allen laws, L(t)∼${\mathit{t}}^{1/3}$ and ${\mathit{t}}^{1/2}$ for conserved and nonconserved scalar order parameters, respectively. For σ<1, the results L(t)∼${\mathit{t}}^{1/(2+\mathrm{\sigma })}$ and ${\mathit{t}}^{1/(1+\mathrm{\sigma })}$, respectively, are obtained. For a vector order parameter, we find L(t)∼${\mathit{t}}^{1/(2+\mathrm{\sigma })}$ and ${\mathit{t}}^{1/\mathrm{\sigma }}$ for conserved and nonconserved fields, respectively, for all σ<2.