Description of periodic and weakly periodic ground states for the modified SOS model on the Cayley tree

Abstract

This paper investigates the periodic and weakly periodic ground states on the Cayley tree of order two and three. Utilizing techniques from statistical mechanics, algebraic graph theory, and group theory, we determine the conditions under which these ground states can exist. Our results demonstrate that the unique structure of the Cayley tree supports a variety of periodic and weakly periodic ground states, each with distinct physical properties. These findings enhance our understanding of phase transitions and critical phenomena in physical systems.