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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