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Lattice Models for Liquid Crystals

  • Ole J. Heilmann
  • Elliott H. Lieb
Chapter

Abstract

A problem in the theory of liquid crystals is to construct a model system which at low temperatures displays long-range orientational order, but not translational order in all directions. We present five lattice models (two two-dimensional and three three-dimensional) of hard-core particles with attractive interactions and prove (using reflection positivity and the Peierls argument) that they have orientational order at low temperatures; the two-dimensional models have no such ordering if the attractive interaction is not present. We cannot prove that these models do not have complete translational order, but their zero-temperature states are such that we are led to conjecture that complete translational order is always absent.

Key Words

Lattice models liquid crystals phase transitions 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Ole J. Heilmann
    • 1
  • Elliott H. Lieb
    • 2
  1. 1.Department of Chemistry, H. C. Ørsted InstituteUniversity of CopenhagenCopenhagenDenmark
  2. 2.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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