title: Renormalization-group theory for the phase-field crystal equation.
abstract: We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal 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-scale 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.
authors.affiliation: Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, Illinois 61801, USA.
authors.forename: Badrinarayan P
authors.initials: BP
authors.lastname: Athreya
authors.forename: Nigel
authors.initials: N
authors.lastname: Goldenfeld
authors.forename: Jonathan A
authors.initials: JA
authors.lastname: Dantzig