Renormalization-group theory for the phase-field crystal equation

2006/02/28 by Badrinarayan P. Athreya, Nigel Goldenfeld, Jonathan A. Dantzig
Computer Science · Materials Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Solidification and crystal growth phenomena #Theoretical and Computational Physics #cond-mat.mtrl-sci #nlin.PS

paper · pdf · doi:10.1103/physreve.74.011601

published as Phys. Rev. E 74, 011601 (2006) · 13 pages, 1 figure, submitted to Phys. Rev. E

arxiv created 2006/06/06 · openalex publication_date 2006/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Lectures on Phase Transitions and the Renormalization Group
• Hydrodynamic fluctuations at the convective instability
• Pattern formation outside of equilibrium
• Mapping molecular models to continuum theories for partially miscible fluids
• Matching Conditions in Atomistic-Continuum Modeling of Materials
• The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory