三角形和蜂窝状排列模型的星-三角对偶性估计
Star-triangle duality estimates for triangular and honeycomb permutation models
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中文总结 AI 辅助
结合星-三角变换，对三角形和蜂窝状晶格上对称群排列模型做对偶性分析，计算受随机张量网络排列模型及早期复制自旋玻璃对偶性分析启发，关键基元是星-三角块，估计出蜂窝状晶格临界键维度为2.634929344884，三角形晶格为1.475661534848。
中文摘要 AI 辅助
我们结合星-三角变换，对三角形和蜂窝状晶格上的对称群排列模型进行对偶性分析。该计算受随机张量网络的排列模型描述以及早期复制自旋玻璃的对偶性分析启发。关键在于有限基元不是裸键，而是星-三角块。我们的分析估计出蜂窝状晶格的临界键维度为2.634929344884，相关单键对偶关系得出三角形晶格的估计值为1.475661534848。
英文摘要
We study a duality analysis in conjunction with the star-triangle transformation for symmetric-group permutation models on the triangular and honeycomb lattices. The calculation is motivated by the permutation-model description of random tensor networks and by earlier duality analyses of replicated spin glasses. The essential point is that the finite-basis unit is not a bare bond but a star-triangle block. Our analysis estimates the critical bond dimension for the honeycomb lattice to be 2.634929344884, and the associated single-bond duality relation yields the triangular-lattice estimate 1.475661534848.
