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Existence of \(p\)-adic quasi Gibbs measure for countable state Potts model on the Cayley tree. (English) Zbl 1281.46062
Summary: We provide a new construction of a measure, called \(p\)-adic quasi Gibbs measure, for countable states of a \(p\)-adic Potts model on the Cayley tree. Such a construction depends on a parameter \(\mathfrak p\) and weights. In a particular case, i.e., if \(\mathfrak p=\exp_ p\), the defined measure coincides with the \(p\)-adic Gibbs measure. In this article, under some condition on weights, we establish the existence of \(p\)-adic quasi Gibbs measures associated with the model. Note that this condition does not depend on the values of the prime \(p\). An analogous fact is not valid when the number of spins is finite.

MSC:
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
82B26 Phase transitions (general) in equilibrium statistical mechanics
12J12 Formally \(p\)-adic fields
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