The Dynamics of The Potts-Bethe Mapping over ${\mathbb{Q}}_p:$ The Case $p\equiv 2(mod3)$

Abstract

In this paper, we study the dynamics of the Potts-Bethe mapping associated with the $p-$adic $q-$state Potts model over the Cayley tree of order three. Namely, we establish the regularity of the Potts-Bethe mapping for the case $p\equiv 2(mod3)$ with $p\ge 5$.

15 pages

References in corpus (3)

• Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree
• On equation $x^q=a$ over $\bq_p$
• Renormalization method in $p$-adic $\lambda$-model on the Cayley tree