ON INHOMOGENEOUS p-ADIC POTTS MODEL ON A CAYLEY TREE
نویسنده
چکیده
We consider a nearest-neighbor inhomogeneous p-adic Potts (with q ≥ 2 spin values) model on the Cayley tree of order k ≥ 1. The inhomogeneity means that the interaction Jxy couplings depend on nearest-neighbors points x, y of the Cayley tree. We study (p− adic) Gibbs measures of the model. We show that (i) if q / ∈ pN then there is unique Gibbs measure for any k ≥ 1 and ∀Jxy with |Jxy | < p . (ii) For q ∈ pN, p ≥ 3 one can choose Jxy and k ≥ 1 such that there exist at least two Gibbs measures which are translation-invariant.
منابع مشابه
On Gibbs Measures of P -adic Potts Model on the Cayley Tree
We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ∈ Qp) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ∈ pN and p ≥ 3 (resp. q ∈ 2N, p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ∈ pN if p ≥ 3 and q ∈ 2N if p = 2.
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