GRADIENT GIBBS MEASURES FOR THE SOS MODEL WITH COUNTABLE VALUES ON A CAYLEY TREE

Abstract : We consider an SOS (solid-on-solid) model, with spin values from the set of all integers, on a Cayley tree of order k ≥ 2 and are interested in translation-invariant gradient Gibbs measures (GGMs) of the model. Such a measure corresponds to a boundary law (a function defined on vertices of the Cayley tree) satisfying a functional equation. In the ferromagnetic SOS case on the binary tree we find up to five solutions to a class of 4-periodic boundary law equations (in particular, some two periodic ones). We show that these boundary laws define up to four distinct GGMs. Moreover, we construct some 3-periodic boundary laws on the Cayley tree of arbitrary order k ≥ 2, which define GGMs different from the 4-periodic ones. Mathematics Subject Classifications (2010). 82B26 (primary); 60K35 (sec-ondary)
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Contributor : Arnaud Le Ny <>
Submitted on : Wednesday, February 20, 2019 - 11:41:48 AM
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  • HAL Id : hal-02037877, version 1
  • ARXIV : 1902.04909

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F Henning, C Kuelske, A Le Ny, U Rozikov. GRADIENT GIBBS MEASURES FOR THE SOS MODEL WITH COUNTABLE VALUES ON A CAYLEY TREE. 2019. ⟨hal-02037877⟩

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