Gradient Gibbs measures of a SOS model on Cayley trees: 4-periodic boundary laws

Abstract

For SOS (solid-on-solid) model with external field and with spin values from the set of all integers, on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (a function defined on vertices of Cayley tree) satisfying an infinite system of functional equations. We give several concrete GGMs which correspond to periodic boundary laws.

arXiv comment16 pages, 2 figures. arXiv admin note: text overlap with arXiv:1902.04909

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Cited by in corpus (1)

• Fixed points of an infinite dimensional operator related to Gibbs measures