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<p>This paper investigates gradient Gibbs measures within the SOS model, obtained via <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>-height periodic boundary laws associated with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(G_{k}^{(2)}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>G</mi> <mrow> <mi>k</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation> (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(G_{k}^{(2)}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>G</mi> <mrow> <mi>k</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation>-boundary law) on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">G</mi> </math></EquationSource> </InlineEquation>-admissible configuration spaces for graphs with infinite symmetric Toeplitz adjacency matrices [<CitationRef CitationID="CR2">2</CitationRef>], focusing on Cayley trees of arbitrary order.</p>

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Gradient Measures on Cayley Trees Associated with Two Periodic Homogeneous and Inhomogeneous Boundary Laws for the SOS Model

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • R. A. Ilyasova

摘要

This paper investigates gradient Gibbs measures within the SOS model, obtained via \(2\) 2 -height periodic boundary laws associated with \(G_{k}^{(2)}\) G k ( 2 ) ( \(G_{k}^{(2)}\) G k ( 2 ) -boundary law) on \(\mathcal {G}\) G -admissible configuration spaces for graphs with infinite symmetric Toeplitz adjacency matrices [2], focusing on Cayley trees of arbitrary order.