Extremality of translation-invariant Gibbs measures for the Potts–SOS model on the Cayley tree
M M Rahmatullaev, M A Rasulova
Abstract
Abstract In this paper, we consider the Potts–SOS model where the spin takes values in the set {0, 1, 2} on the Cayley tree of order two. We describe all the translation-invariant splitting Gibbs measures (GMs) for this model in some conditions. Moreover, we investigate whether these GMs are extremal or non-extremal in the set of all GMs.
Topics & Concepts
MathematicsTree (set theory)Set (abstract data type)CombinatoricsOrder (exchange)Cayley graphGibbs measureDiscrete mathematicsGenerating set of a groupPure mathematicsMeasure (data warehouse)Tree networkTheoretical and Computational PhysicsMarkov Chains and Monte Carlo MethodsStochastic processes and statistical mechanics