2014/11/21 by Christof Kuelske, C. Kuelske, Kuelske, C. +2
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60K35 #82B26 #FOS: Physical sciences #Mathematical Physics (math-ph) #Protein Structure and Dynamics #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics #math-ph #math.MP #msc:60K35 #msc:82B26
paper · pdf · doi:10.48550/arxiv.1411.5886
23 pages
arxiv created 2014/11/21 · openalex publication_date 2014/11/21 · arxiv updated 2014/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the SOS (solid-on-solid) model, with spin values 0,1,2, on the Cayley tree of order two (binary tree). We treat both ferromagnetic and antiferromagnetic coupling, with interactions which are proportional to the absolute value of the spin differences. We present a classification of all translation-invariant phases (splitting Gibbs measures) of the model: We show uniqueness in the case of antiferromagnetic interactions, and existence of up to seven phases in the case of ferromagnetic interactions, where the number of phases depends on the interaction strength. Next we investigate whether these states are extremal or non-extremal in the set of all Gibbs measures, when the coupling strength is varied, whenever they exist. We show that two states are always extremal, two states are always non-extremal, while three of the seven states make transitions between extremality and non-extremality. We provide explicit bounds on those transition values, making use of algebraic properties of the models, and an adaptation of the method of Martinelli, Sinclair, Weitz.