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

Mireille Bousquet-Mélou Gilles Schaeffer 1
1 ADAGE - Applying discrete algorithms to genomics
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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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Submitted on : Tuesday, September 26, 2006 - 2:55:12 PM
Last modification on : Friday, February 4, 2022 - 3:23:43 AM

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  • HAL Id : inria-00101064, version 1

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Mireille Bousquet-Mélou, Gilles Schaeffer. The degree distribution in bipartite planar maps: applications to the Ising model. [Intern report] A02-R-212 || bousquet-melou02a, 2002, 32 p. ⟨inria-00101064⟩

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