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The degree distribution in bipartite planar maps: applications to the Ising model

Identifieur interne : 004C38 ( Hal/Curation ); précédent : 004C37; suivant : 004C39

The degree distribution in bipartite planar maps: applications to the Ising model

Auteurs : Mireille Bousquet-Mélou ; Gilles Schaeffer [France]

Source :

RBID : Hal:inria-00101064

Descripteurs français

mix :
- bipartite maps, cartes aléatoires, cartes biparties, graphes planaires, ising model, modèle d'ising, planar graphs, random maps.

Abstract

We characterize the generating function of bipartite planar maps counted according to the degree distribution of their black and white vertices. This result is applied to the solution of the hard particle and Ising models on random planar lattices. We thus recover and extend some results previously obtained by means of matrix integrals. Proofs are purely combinatorial and rely on the idea that planar maps are conjugacy classes of trees. In particular, these trees explain why the solutions of the Ising and hard particle models on maps of bounded degree are always algebraic.

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https://hal.inria.fr/inria-00101064

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Le document en format XML

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The degree distribution in bipartite planar maps: applications to the Ising model

The degree distribution in bipartite planar maps: applications to the Ising model

Source :

Descripteurs français

Abstract

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Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

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