On set of p-adic Gibbs measures for the countable state 1D SOS model
Аннотация
Abstract Previous studies mainly focused on the p -adic Potts model with countable spin values, demonstrating that this model has only one p -adic Gibbs measure. Furthermore, it was shown that the model exhibits a phase transition in the set of generalized Gibbs measures. A challenge remained to find a countable spin p -adic model where the set of all p -adic Gibbs measures would include at least two elements. In this paper, we have examined the one-dimensional p -adic SOS model and demonstrated that the set of all p -adic Gibbs measures has continuum cardinality. This phenomenon has not been observed in countable state p -adic Potts models. Our result addresses the aforementioned problem affirmatively. To establish this finding, we employed a p -adic dynamical system related to the p -adic Gibbs measure through the renormalization group technique. Our analysis confirms the occurrence of a phase transition for the model in question.