Fermionic solution of the Andrews-Baxter-Forrester model. I. Unification of TBA and CTM methods |
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Authors: | S. Ole Warnaar |
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Affiliation: | (1) Mathematics Department, Universit of Melbourne, 3052 Parkville, Victoria, Australia |
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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 l,1(r–l,r)(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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Keywords: | Corner transfer matrices thermodynamic Bethe Ansatz ABF model one-dimensional Fermi gas Rogers-Ramanujan identities |
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