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

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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.
32 pages, 15 figures

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Combinatorics, Mathematical Physics, 05C30 (Primary), 81T18, 82B20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/65543

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0211070
 http://arxiv.org/abs/math/0211070

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arXiv