1204.2603 (Farrukh Mukhamedov)

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

Farrukh Mukhamedov

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 $\frak{p}$ and wights. In particular case, i.e. if $\frak{p}=\exp_p$, 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.

View original: http://arxiv.org/abs/1204.2603