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hal-00004425, version 1

Entropy-driven phase transition in a polydisperse hard-rods lattice system

Dmitry Ioffe () 1, Yvan Velenik () 2, Milos Zahradnik () 3

Abstract: We study a system of rods on the 2d square lattice, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N=2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals.

  • 1:  Faculty of Industrial Engineering
  • Technion - Israel Institute of Technology
  • 2:  Laboratoire de Mathématiques Raphaël Salem (LMRS)
  • CNRS : UMR6085 – Université de Rouen
  • 3:  Faculty of Mathematics and Physics
  • Charles University
  • Domain : Mathematics/Probability
    Mathematics/Combinatorics
    Mathematics/Mathematical Physics
  • Keywords : Hard-rods – monomer-dimer model – nematic order – liquid crystal – phase transition – hard-core
 
  • hal-00004425, version 1
  • http://hal.archives-ouvertes.fr/hal-00004425
  • oai:hal.archives-ouvertes.fr:hal-00004425
  • From: Yvan Velenik <>
  • Submitted on: Friday, 11 March 2005 18:03:04
  • Updated on: Friday, 11 March 2005 18:06:33