Star-triangle duality estimates for triangular and honeycomb permutation models
arXiv:2607.14917
The paper applies a star‑triangle transformation combined with duality analysis to symmetric‑group permutation models on triangular and honeycomb lattices, estimating the critical bond dimensions for these lattices.
Abstract
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.
14 pages