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<p>We show that the <i>i</i>-dimensional plaquette random-cluster model with coefficients in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {Z}_q\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation> is dual to a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((d-i)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>d</mi> <mo>-</mo> <mi>i</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dimensional plaquette random cluster model. In addition, we explore boundary conditions, infinite volume limits, and uniqueness for these models. For previously known results, we provide new proofs that rely more on the tools of algebraic topology.</p>

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Some Properties of the Plaquette Random-Cluster Model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月10日

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  • Paul Duncan,
  • Benjamin Schweinhart

摘要

We show that the i-dimensional plaquette random-cluster model with coefficients in \(\mathbb {Z}_q\) Z q is dual to a \((d-i)\) ( d - i ) -dimensional plaquette random cluster model. In addition, we explore boundary conditions, infinite volume limits, and uniqueness for these models. For previously known results, we provide new proofs that rely more on the tools of algebraic topology.