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New Q Matrices and Their Functional Equations for the Eight Vertex Model at Elliptic Roots of Unity

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Abstract

The Q matrix invented by Baxter in 1972 to solve the eight vertex model at roots of unity exists for all values of N, the number of sites in the chain, but only for a subset of roots of unity. We show in this paper that a new Q matrix, which has recently been introduced and is non zero only for N even, exists for all roots of unity. In addition we consider the relations between all of the known Q matrices of the eight vertex model and conjecture functional equations for them.

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Authors and Affiliations

  1. Physics Department, University of Wuppertal, 42097, Wuppertal, Germany

    Klaus Fabricius

  2. C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, NY, 11794-3840, USA

    Barry M. McCoy

Authors
  1. Klaus Fabricius
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  2. Barry M. McCoy
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Correspondence to Klaus Fabricius.

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Fabricius, K., McCoy, B.M. New Q Matrices and Their Functional Equations for the Eight Vertex Model at Elliptic Roots of Unity. J Stat Phys 134, 643–668 (2009). https://doi.org/10.1007/s10955-009-9692-6

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  • DOI: https://doi.org/10.1007/s10955-009-9692-6

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