Existence of $P$-adic quasi Gibbs measure for countable state Potts model on the Cayley tree

Abstract

In the present paper we provide a new construction of measure, called $p$-adic quasi Gibbs measure, for countable state of $p$-adic Potts model on the Cayley tree. Such a construction depends on a parameter $\mathfrak{p}$ and wights. In particular case, i.e. if $\mathfrak{p}={\exp }_p$, the defined measure coincides with $p$-adic Gibbs measure. In this paper, 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 values of the prime $p$. An analogues fact is not valid when the number of spins is finite.

arXiv comment13 pages

References in corpus (1)

• Application of p-adic analysis to models of spontaneous breaking of the replica symmetry