A new eight vertex model and higher dimensional, multiparameter generalizations

Abstract

We study statistical models, specifically transfer matrices corresponding to a multiparameter hierarchy of braid matrices of $(2n)^2\times(2n)^2$ dimensions with $2n^2$ free parameters $(n=1,2,3,...)$. The simplest, $4\times 4$ case is treated in detail. Powerful recursion relations are constructed giving the dependence on the spectral parameter $\theta$ of the eigenvalues of the transfer matrix explicitly at each level of coproduct sequence. A brief study of higher dimensional cases ($n\geq 2$) is presented pointing out features of particular interest. Spin chain Hamiltonians are also briefly presented for the hierarchy. In a long final section basic results are recapitulated with systematic analysis of their contents. Our eight vertex $4\times 4$ case is compared to standard six vertex and eight vertex models.