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The Nematic Phase of a System of Long Hard Rods

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Abstract

We consider a two-dimensional lattice model for liquid crystals consisting of long rods interacting via purely hard core interactions, with two allowed orientations defined by the underlying lattice. We rigorously prove the existence of a nematic phase, i.e., we show that at intermediate densities the system exhibits orientational order, either horizontal or vertical, but no positional order. The proof is based on a two-scales cluster expansion: we first coarse grain the system on a scale comparable with the rods’ length; then we express the resulting effective theory as a contour’s model, which can be treated by Pirogov-Sinai methods.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS-Université de Rouen, Av. de l’Université, BP.12, Technopôle du Madrillet, 76801, Saint-Étienne-du-Rouvray, France

    Margherita Disertori

  2. Dipartimento di Matematica e Fisica, Università di Roma Tre, L.go S. L. Murialdo 1, 00146, Roma, Italy

    Alessandro Giuliani

Authors
  1. Margherita Disertori
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  2. Alessandro Giuliani
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Correspondence to Alessandro Giuliani.

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Communicated by H. Spohn

Dedicated to the 70 th birthday of Giovanni Gallavotti

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Disertori, M., Giuliani, A. The Nematic Phase of a System of Long Hard Rods. Commun. Math. Phys. 323, 143–175 (2013). https://doi.org/10.1007/s00220-013-1767-1

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