Gradient Gibbs measures of a SOS model on Cayley trees: 4-periodic boundary laws
F. H. Haydarov, U.A. Rozikov
TL;DR
This paper constructs gradient Gibbs measures for an SOS model with external field on Cayley trees, linking these measures to boundary laws satisfying functional equations, and provides explicit examples of periodic boundary laws.
Contribution
It introduces a method to obtain gradient Gibbs measures for the SOS model on Cayley trees via boundary laws and presents concrete examples of periodic boundary laws.
Findings
Constructed explicit gradient Gibbs measures for the SOS model.
Linked boundary laws to solutions of functional equations.
Provided examples of 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.
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