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<p>By modifying the automaton used by Pönitz and Tittman [<CitationRef CitationID="CR9">9</CitationRef>], principally by enabling multiple choices for state transitions through various simplification strategies, and considering states with a maximum size-loop of 26 (compared to 22 in their work), we obtain 2.662343 as an upper bound for the connective constant on the square lattice <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10955_2025_3542_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Z}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>.</p>

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New Upper Bound for the Connective Constant for square-lattice Self-Avoiding Walks

  • 期刊论文

  • 发表日期：

    2025年10月31日

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  • Olivier Couronné

摘要

By modifying the automaton used by Pönitz and Tittman [9], principally by enabling multiple choices for state transitions through various simplification strategies, and considering states with a maximum size-loop of 26 (compared to 22 in their work), we obtain 2.662343 as an upper bound for the connective constant on the square lattice \(\mathbb {Z}^2\) Z 2 .