Potts model on infinite graphs and the limit of chromatic polynomials

Details Potts model on infinite graphs and the limit of chromatic polynomials Potts model on infinite graphs and the limit of chromatic polynomials

2002-01-11

arxiv.org/abs/cond-mat/0201183v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1007/s00220-002-0789-x

Given an infinite graph $\GI$ quasi-transitive and amenable with maximum degree $\D$, we show that reduced ground state degeneracy per site $W_r(\GI,q)$ of the q-state antiferromagnetic Potts model at zero temperature on $\GI$ is analytic in the variable 1/q, whenever $|2\D e^3/q|< 1$. This result proves, in an even stronger formulation, a conjecture originally sketched in [KE] (Kim and Enting, 1979) and explicitly formulated in [ST] (Shrock and Tsai,1997), based on which a sufficient condition for $W_r(\GI,q)$ to be analytic at 1/q=0 is that $\GI$ is a regular lattice.

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