Potts model on infinite graphs and the limit of chromatic polynomials

الأصل · EN

Given an infinite graph quasi-transitive and amenable with maximum degree, we show that reduced ground state degeneracy per site Wᵣ(,q) of the q-state antiferromagnetic Potts model at zero temperature on is analytic in the variable 1/q, whenever |2 e³/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 Wᵣ(,q) to be analytic at 1/q=0 is that is a regular lattice.