Existence of p-adic quasi Gibbs measure for countable state Potts model on the Cayley tree
Department of Computational & Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box, 141, 25710, Kuantan, Pahang, Malaysia
Journal of Inequalities and Applications 2012, 2012:104 doi:10.1186/1029-242X-2012-104Published: 8 May 2012
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 and wights. In particular case, i.e., if , 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.
Mathematics Subject Classification: 46S10; 82B26; 12J12.