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.

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

References in corpus (3)

• Nonexistence of random gradient Gibbs measures in continuous interface models in $d=2$
• Gradient Gibbs measures and fuzzy transformations on trees
• Existence of gradient Gibbs measures on regular trees which are not translation invariant

Cited by in corpus (1)

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