The result of Pereira Phys. Rev. E 63 , 061809 (2001) does not contradict previous work, but rather complements it. Both this work and previous work show there is no reason to suspect that a circular interface in a hexagonal Wigner-Seitz cell is stable to small perturbations, whether they are hexagonal or elliptical. The elliptical perturbation is on the downward energy pathway from a perfectly circular interface to a hexagonally modulated interface. Finally, my thin film conclusions are shown to be valid using an independent method.
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