Abstract
The partition-functions-per-siteκ of several two-dimensional models (notably the eight-vertex, self-dual Potts and hard-hexagon models) can be easily obtained by using an inversion relation for local transfer matrices, together with symmetry and analyticity properties. This technique is discussed, the analyticity properties compared, and some equivalences (and nonequivalences) pointed out. In particular, the critical hard-hexagon model is found to have the sameκ as the self-dualq-state Potts model, withq=(3 + √5)/2 = 2.618 .... The Temperley-Lieb equivalence between the Potts and six-vertex models is found to fail in certain nonphysical antiferromagnetic cases.
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Baxter, R.J. The inversion relation method for some two-dimensional exactly solved models in lattice statistics. J Stat Phys 28, 1–41 (1982). https://doi.org/10.1007/BF01011621
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DOI: https://doi.org/10.1007/BF01011621