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

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

2008-02-14

arxiv.org/abs/0802.2107v2

Phys. Rev. E 79, 021116 (2009)

Physics

Condensed Matter

Other Condensed Matter

36 pages, 7 figures; v2: added additional clarifications and a discussion on how this method differs from the MIB-approach

Scientific paper

10.1103/PhysRevE.79.021116

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.

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