Vortices in two-dimensional nematics. (English) Zbl 1187.82035

Summary: We study a two-dimensional model describing spatial variations of orientational ordering in nematic liquid crystals. In particular, we show that the spatially extended Onsager-Maier-Saupe free energy may be decomposed into Landau-de Gennes-type and relative entropy-type contributions. We then prove that in the high concentration limit the states of the system display characteristic vortex-like patterns and derive an asymptotic expansion for the free energy of the system.


82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
82B26 Phase transitions (general) in equilibrium statistical mechanics
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
76A15 Liquid crystals
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