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Laboratoire de Mathématiques Raphaël Salem - Collection HAL |  |
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Laboratoire de Mathématiques Raphaël Salem - Collection HAL | |
| HAL : hal-00004425, version 1 |
| arXiv : math.PR/0503222 |
| Fiche détaillée |  Récupérer au format |
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| Entropy-driven phase transition in a polydisperse hard-rods lattice system |
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| Dmitry Ioffe 1Yvan Velenik 2 |
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| (11/03/2005) |
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| 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. |
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| 1 : | Faculty of Industrial Engineering |
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Technion - Israel Institute of Technology |
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| 2 : | Laboratoire de Mathématiques Raphaël Salem (LMRS) |
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CNRS : UMR6085 – Université de Rouen |
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| 3 : | Faculty of Mathematics and Physics |
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Charles University |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Combinatoire Mathématiques/Physique mathématique |
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| Hard-rods – monomer-dimer model – nematic order – liquid crystal – phase transition – hard-core |
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| hal-00004425, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00004425 | |
| oai:hal.archives-ouvertes.fr:hal-00004425 | |
| Contributeur : Yvan Velenik | |
| Soumis le : Vendredi 11 Mars 2005, 18:03:04 | |
| Dernière modification le : Vendredi 11 Mars 2005, 18:06:33 | |
