Christian Korff 2005 J. Phys. A: Math. Gen. 38 47 doi:10.1088/0305-4470/38/1/003
Christian Korff
Show affiliationsThe spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even roots of unity and an odd number of sites the eigenvalues contain two linear independent solutions to Baxter's TQ-equation corresponding to the Bethe ansatz equations above and below the equator. In contrast, one finds for even spin-chains only one linear independent solution and complete strings. The other main result is the proof of a previous conjecture on the degeneracies of the six-vertex model at roots of unity. The proof rests on the derivation of a functional equation for the auxiliary matrices which is closely related to a functional equation for the eight-vertex model conjectured by Fabricius and McCoy.
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
15A30 Algebraic systems of matrices (See also 16S50, 20Gxx, 20Hxx)
Issue 1 (7 January 2005)
Received 17 August 2004, in final form 2 November 2004
Published 8 December 2004
Christian Korff 2005 J. Phys. A: Math. Gen. 38 47
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