| Summary: | In the present paper we consider the countable state p-adic Potts
model on Z+. A main aim is to establish the existence of the strong phase
transition for the model. In our study, we essentially use one dimensionality
of the model. To prove the existence of the phase transition, we reduce the
problem to the investigation of an in�nite-dimensional nonlinear equation. We
�nd a condition on weights to show that the derived equation has two solutions.
We show that measures corresponding to �rst and second solutions are a p-adic
Gibbs and generalized p-adic Gibbs measures, respectively. Moreover, it is proved
that the p-adic Gibbs measure is bounded, and the generalized one is not
bounded. This implies the existence of the strong phase transition. Note that
it turns out that the obtained condition does not depend on values of the prime
p and, therefore, an analogous fact is not true when the number of spins is �nite.
Note that, in the usual real case, if one considers a one-dimensional translation-
invariant model with nearest neighbor interaction, then such a model does not
exhibit a phase transition. Nevertheless, we should stress that our model exhibits
a unique p-adic Gibbs measure.
|
|---|