Star–Triangle Duality Estimates for Triangular and Honeycomb Permutation Models

This is the authors' abstract. We don't add key points for this paper.

We study a duality analysis in conjunction with the star–triangle transformation for symmetric-group permutation models on 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.