p-Adic Quasi Gibbs Measures for the Three-State SOS Model with an External Field on a Cayley Tree

Key Points

• The research aims to analyze the quasi Gibbs measures in a three-state SOS model on a Cayley tree with an external field. It seeks to identify the conditions leading to phase transitions.
• Derived functional equations corresponding to the three-state SOS model
• Investigated translation-invariant p-adic quasi Gibbs measures
• Analyzed the boundedness of measures to establish phase transitions
• Identified explicit forms of TIpQGMs for the binary Cayley tree
• Established a condition for the existence of phase transitions based on the measures
• Demonstrated the relationship between the external field and phase transition behaviors

Abstract