Multiparameter Statistical Models from 𝑁2×𝑁2 Braid Matrices: Explicit Eigenvalues of Transfer Matrices T(𝑟), Spin Chains, Factorizable Scatterings for All 𝑁 - B. Abdesselam; A. Chakrabarti (Advances in Mathematical Physics)
For a class of multiparameter statistical models based on 𝑁2×𝑁2 braid matrices, the eigenvalues of the transfer matrix 𝐓(𝑟) are obtained explicitly for all (𝑟,𝑁). Our formalism yields them as solutions of sets of linear equations with simple constant coefficients. The role of zero-sum multiplets constituted in terms of roots of unity is pointed out, and their origin is traced to circular permutations of the indices in the tensor products of basis states induced by our class of 𝐓(𝑟) matrices. The role of free parameters, increasing as 𝑁2 with N, is emphasized throughout. Spin chain Hamiltonians are constructed and studied for all N. Inverse Cayley transforms of the Yang-Baxter matrices corresponding to our braid matrices are obtained for all N. They provide potentials for factorizable S-matrices. Main results are summarized, and perspectives are indicated in the concluding remarks.