Lattice models for liquid crystals

Ole J. Heilmann, Elliott H. Lieb

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43 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)679-693
Number of pages15
JournalJournal of Statistical Physics
Issue number6
StatePublished - Jun 1979

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Lattice models
  • liquid crystals
  • phase transitions


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