Potts Model on Infinite Graphs and the Limit of Chromatic Polynomials |
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| Authors: | Aldo Procacci Benedetto Scoppola Victor Gerasimov |
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| Affiliation: | 1.Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Ant?nio Carlos, 6627, Caixa Postal 702, 30161-970, Belo Horizonte, MG Brazil. E-mail: aldo@mat.ufmg.br; victor@mat.ufmg.br,BR;2.Dipartimento di Matematica, Universitá ``La Sapienza' di Roma, Piazzale A. Moro 2, 00185 Roma, Italy. E-mail: benedetto.scoppola@roma1.infn.it,IT |
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| Abstract: | Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy per site W r (𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe 3 /q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated in [16 and 19], based on which a sufficient condition for W r (𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice. Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003 RID="*" ID="*" Partially supported by CNPq (Brazil) RID="**" ID="**" Partially supported by CNR, G.N.F.M. (Italy) Communicated by H. Spohn |
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