Abstract
We consider a nearest-neighbor p-adic λ-model with spin values ±1 on the Cayley tree of order k⩾1. We prove that a p-adic Gibbs measure is unique for p⩾3. If p=2 then we find a condition which guarantees uniqueness of p-adic Gibbs measure. Besides, the results are applied to the p-adic Ising model.
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