GRADIENT GIBBS MEASURES FOR THE SOS MODEL WITH COUNTABLE VALUES ON A CAYLEY TREE
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Abstract
We investigate an SOS (solid-on-solid) model on a Cayley tree of rank k 2 with spin values from the set of all integers and are interested in the model's translation-invariant gradient Gibbs measures (GGMs). A measure of this type relates to a boundary law (a function defined on the vertices of the Cayley tree) that solves a functional equation. On the binary tree, we discover up to five solutions to a class of 4-periodic boundary law equations (specifically, certain two periodic ones).
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