New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity

Details New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity

2008-09-16

arxiv.org/abs/0809.2802v1

Physics

Condensed Matter

Statistical Mechanics

20 pages, 2 Postscript figures

Scientific paper

10.1007/s10955-009-9692-6

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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