Abstract
The partition function of the O(n) loop model on the honeycomb lattice is mapped to that of the O(n) loop model on the 3–12 lattice. Both models share the same operator content and thus critical exponents. The critical points are related via a simple transformation of variables. When n = 0 this gives the recently found exact value μ = 1.711041... for the connective constant of self-avoiding walks on the 3–12 lattice. The exact critical points are recovered for the Ising model on the 3–12 lattice and the dual asanoha lattice at n = 1.
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Batchelor, M.T. The O(n) Loop Model on the 3–12 Lattice. Journal of Statistical Physics 92, 1203–1208 (1998). https://doi.org/10.1023/A:1023065215233
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DOI: https://doi.org/10.1023/A:1023065215233