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Abstract <p> In present paper we study <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1119_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic quasi Gibbs measures for the SOS model on the Cayley tree of order two. Using the boundedness of translation-invariant and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1119_Article_IEq3.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_k^{(2)}\)</EquationSource> </InlineEquation>-periodic <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1119_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic quasi Gibbs measures, the existence of a phase transition is proven. </p>

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\(p\)-Adic Quasi Gibbs Measures for the SOS Model on the Cayley Tree of Order Two

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • M. M. Rahmatullaev,
  • O. U. Akhmedov,
  • A. M. Tukhtabaev

摘要

Abstract

In present paper we study \(p\) -adic quasi Gibbs measures for the SOS model on the Cayley tree of order two. Using the boundedness of translation-invariant and \(G_k^{(2)}\) -periodic \(p\) -adic quasi Gibbs measures, the existence of a phase transition is proven.