Renormalization group theory for the phase field crystal equation

Details Renormalization group theory for the phase field crystal equation Renormalization group theory for the phase field crystal equation

2006-02-15

arxiv.org/abs/nlin/0602034v2

Phys. Rev. E 74, 011601 (2006)

Nonlinear Sciences

Pattern Formation and Solitons

13 pages, 1 figure, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.74.011601

We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two dimensional phase field crystal (PFC) model by a variety of renormalization group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple scales techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.

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