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Fermionic solution of the Andrews-Baxter-Forrester model. I. Unification of TBA and CTM methods

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Abstract

The problem of computing the one-dimensional configuration sums of the ABF model in regime III is mapped onto the problem of evaluating the grandcanonical partition function of a gas of charged particles obeying certain fermionic exclusion rules. We thus obtain a newfermionic method to compute the local height probabilities of the model. Combined with the originalbosonic approach of Andrews, Baxter, and Forrester, we obtain a new proof of (some of) Melzer's polynomial identities. In the infinite limit these identities yield Rogers-Ramanujan type identities for the Virasoro characters χ (r−l,r)l,1 (q) as conjectured by the Stony Brook group. As a result of our work the corner transfer matrix and thermodynamic Bethe Ansatz approaches to solvable lattice models are unified.

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  1. Mathematics Department, Universit of Melbourne, 3052, Parkville, Victoria, Australia

    S. Ole Warnaar

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Ole Warnaar, S. Fermionic solution of the Andrews-Baxter-Forrester model. I. Unification of TBA and CTM methods. J Stat Phys 82, 657–685 (1996). https://doi.org/10.1007/BF02179790

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