A new eight vertex model and higher dimensional, multiparameter generalizations

TL;DR

This paper introduces a new multiparameter hierarchy of braid matrices leading to an eight vertex model, providing explicit eigenvalue relations, higher-dimensional generalizations, and comparisons with standard models.

Contribution

It develops a novel multiparameter hierarchy of braid matrices and explicitly constructs transfer matrices and eigenvalues for the new eight vertex model, extending to higher dimensions.

Findings

Explicit eigenvalue dependence on spectral parameter at each hierarchy level

Construction of transfer matrices for higher-dimensional models

Comparison with standard six and eight vertex models

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.