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<p>This paper represents a continuation of our previous work, where the Boltzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories. Here, we focus on deriving solutions for the Boltzmann weights of the Interaction-Round the Face lattice model, specifically, the unrestricted face model, based on the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25641_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="fraktur">su</mi> <msub> <mfenced close=")" open="("> <mn>3</mn> </mfenced> <mi>k</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">\( \mathfrak{su}{(3)}_k \)</EquationSource> </InlineEquation> affine Lie algebra. The admissibility conditions are defined by the adjoint representation. We find the BWs by determining the quantum <i>R</i> matrix of the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25641_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="67" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>U</mi> <mi>q</mi> </msub> <mfenced close=")" open="("> <mrow> <mi mathvariant="fraktur">sl</mi> <mfenced close=")" open="("> <mn>3</mn> </mfenced> </mrow> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( {U}_q\left(\mathfrak{sl}(3)\right) \)</EquationSource> </InlineEquation> quantum algebra in the adjoint representation and then applying the so-called Vertex-IRF correspondence. The Vertex-IRF correspondence defines the BWs of IRF models in terms of <i>R</i> matrix elements.</p>

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On different approaches to IRF lattice models. Part II

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月27日

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  • Vladimir Belavin,
  • Doron Gepner,
  • J. Ramos Cabezas,
  • Boris Runov

摘要

This paper represents a continuation of our previous work, where the Boltzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories. Here, we focus on deriving solutions for the Boltzmann weights of the Interaction-Round the Face lattice model, specifically, the unrestricted face model, based on the su 3 k \( \mathfrak{su}{(3)}_k \) affine Lie algebra. The admissibility conditions are defined by the adjoint representation. We find the BWs by determining the quantum R matrix of the U q sl 3 \( {U}_q\left(\mathfrak{sl}(3)\right) \) quantum algebra in the adjoint representation and then applying the so-called Vertex-IRF correspondence. The Vertex-IRF correspondence defines the BWs of IRF models in terms of R matrix elements.