Superdiffusion-like behavior in zero-temperature coarsening of the $d=3$ Ising model

One key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent $\alpha =1\mathrm{/}2$ is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with $\alpha <1\mathrm{/}2$ was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations of lattice sizes up to $L=2048$ employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth law – but surprisingly, at still later times domains even grow superdiffusively, i.e., with $\alpha >1\mathrm{/}2$. We argue that this new problem is possibly caused by sponge-like structures emerging at early times.