p-adic quasi-Gibbs measures for the three-state SOS model on the binary tree

Key Points

• New translation-invariant p-adic quasi-Gibbs measures have been established, expanding the existing theories.
• The boundedness of these measures has been proven, ensuring their usability in further applications.
• A phase transition occurs when specific conditions on p and $ heta_s$ are met, suggesting critical phenomena in the model.
• This research contributes to understanding probabilistic measures on trees, crucial in statistical mechanics.