General two-order-parameter Ginzburg-Landau model with quadratic and quartic interactions

I. P. Ivanov
Phys. Rev. E 79, 021116 – Published 17 February 2009

Abstract

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.

    • Received 26 February 2008

    DOI:https://doi.org/10.1103/PhysRevE.79.021116

    ©2009 American Physical Society

    Authors & Affiliations

    I. P. Ivanov*

    • Interactions Fondamentales en Physique et en Astrophysique, Université de Liège, Allée du 6 Août 17, bâtiment B5a, B-4000 Liège, Belgium and Sobolev Institute of Mathematics, Koptyug avenue 4, 630090 Novosibirsk, Russia

    • *Igor.Ivanov@ulg.ac.be

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    Issue

    Vol. 79, Iss. 2 — February 2009

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