Ground States and Gibbs Measures for the SOS Model with an External Field and Countable Set of Spin Values on a Cayley Tree

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发表日期：

2024年11月1日

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Muzaffar M. Rahmatullaev,
Bunyod U. Abraev

摘要

Abstract

In the paper, we consider the solid-on-solid (SOS) model with nearest-neighbor interactions, where the spin takes values in the integers on the Cayley tree of order two. We study the translation-invariant, periodic and non-periodic ground states for the model. Moreover, we describe the ground states and verify the Peierls condition for the model. Using a contour argument, we show the existence of a countable distinct Gibbs measures.