2008/01/26 by Igor Ivanov, I. P. Ivanov · 1 citation
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum optics and atomic interactions #cond-mat.other #cond-mat.supr-con
paper · pdf · doi:10.1103/physreve.79.021116
published as Phys. Rev. E 79, 021116 (2009) · 36 pages, 7 figures; v2: added additional clarifications and a discussion on how this method differs from the MIB-approach
openalex publication_date 2009/02/17 · arxiv created 2009/03/08 · arxiv updated 2015/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Ginzburg-Landau model with two-order parameters appears in many condensed-matter problems. However, even for scalar order parameters, the most general U(1)-symmetric Landau potential with all quadratic and quartic terms contains 13 independent coefficients and cannot be minimized with straightforward algebra. Here, we develop a geometric approach that circumvents this computational difficulty and allows one to study properties of the model without knowing the exact position of the minimum. In particular, we find the number of minima of the potential, classify explicit symmetries possible in this model, establish conditions when and how these symmetries are spontaneously broken, and explicitly describe the phase diagram.