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Phase transition of mixed type \(p\)-adic \({\lambda}\)-Ising model on Cayley tree. (English) Zbl 1421.82004
Summary: In the present paper, we consider an interaction of the nearest-neighbors and next nearest-neighbors for the mixed type \(p\)-adic \({\lambda}\)-Ising model with spin values \(\{-1, +1\}\) on the Cayley tree of order two. We obtained the uniqueness and existence of the \(p\)-adic quasi Gibbs measures for the model. Thereafter, as a main result, we proved the occurrence of phase transition for the \(p\)-adic \({\lambda}\)-Ising model on the Cayley tree of order two. To establish the results, we employed some properties of \(p\)-adic numbers. Therefore, our results are not valid in the real case.

MSC:
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
05C05 Trees
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