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

In the present article, 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 p and wights. In particular case, i.e., if_p = exp_p, the defined measure coincides with 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 values of the prime p. An analogues fact is not valid when the number of spins is finite.