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| HAL : hal-00484977, version 2 |
| arXiv : 1005.3609 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (20-05-2010) | v2 (11-06-2010) |
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| Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices |
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Jesper Jacobsen 1 |
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| (19/05/2010) |
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| We present an efficient algorithm for computing the partition function of the q-colouring problem (chromatic polynomial) on regular two-dimensional lattice strips. Our construction involves writing the transfer matrix as a product of sparse matrices, each of dimension ~ 3^m, where m is the number of lattice spacings across the strip. As a specific application, we obtain the large-q series of the bulk, surface and corner free energies of the chromatic polynomial. This extends the existing series for the square lattice by 32 terms, to order q^{-79}. On the triangular lattice, we verify Baxter's analytical expression for the bulk free energy (to order q^{-40}), and we are able to conjecture exact product formulae for the surface and corner free energies. |
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| 1 : | Laboratoire de Physique Théorique de l'ENS (LPTENS) |
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CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris |
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| Domaine | : | Physique/Matière Condensée/Mécanique statistique Physique/Physique mathématique Mathématiques/Physique mathématique |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00484977, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00484977 | |
| oai:hal.archives-ouvertes.fr:hal-00484977 | |
| Contributeur : Jesper Jacobsen | |
| Soumis le : Jeudi 10 Juin 2010, 10:55:25 | |
| Dernière modification le : Vendredi 11 Juin 2010, 14:48:57 | |
