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Multiparameter statistical models from N**2 x N**2 braid matrices: Explicit eigenvalues of transfer matrices T**(r), spin chains, factorizable scatterings for all N

Jun, 2008
19 pages
Published in:
  • Adv.Math.Phys. 2012 (2012) 193190
e-Print:
DOI:
Report number:
  • CPHT-RR039-06-08
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Abstract: (arXiv)
For a class of multiparameter statistical models based on N2×N2N^2\times N^2 braid matrices the eigenvalues of the transfer matrix T(r){\bf T}^{(r)} are obtained explicitly for all (r,N)(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){\bf T}^{(r)} matrices. The role of free parameters, increasing as N2N^2 with NN, is emphasized throughout. Spin chain Hamiltonians are constructed and studied for all NN. Inverse Cayley transforms of Yang-Baxter matrices corresponding to our braid matrices are obtained for all NN. They provide potentials for factorizable SS-matrices. Main results are summarized and perspectives are indicated in the concluding remarks.
Note:
  • 19 pages, 1 figure