Article

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

M. M. RahmatullaevDepartment of Mathematics, Uzbekistan University, 100007, Tashkent, UzbekistanBunyod U. AbraevChirchik State Pedagogical University, 111702, Chirchik, Tashkent region, Uzbekistan

Lobachevskii Journal of Mathematicsjournal2024en

ABI

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.

Topics

Quantum chaos and dynamical systems Opinion Dynamics and Social Influence Theoretical and Computational Physics

Identifiers

DOI: 10.1134/s1995080224600961

Citations and references

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