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

A new eight vertex model and higher dimensional, multiparameter generalizations