Abstract
The partition function of theN-state Superintegrable chiral Potts model is obtained exactly and explicitly (if not completely rigorously) for a finite lattice with particular boundary conditions. This yields the bulk and surface free energies, and horizontal and vertical correlation lengths and interfacial tensions. The critical exponents are α=1−2/N,μ hor=υhor=2/N, and μvert=υvert=1, and the finite-size corrections are obtained at criticality. The eigenvalue spectrum of the column-to-column transfer matrix is that of a direct product ofN byN matrices. Inverting this matrix gives a related solvable model which is a generalization of the free-fermion model. The associated Hamiltobian has a very simple form, suggesting there may be a more direct algebraic method (perhaps a generalized Clifford algebra) for obtaining its eigenvalues.
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Baxter, R.J. Superintegrable chiral Potts model: Thermodynamic properties, an “inverse” model, and a simple associated Hamiltonian. J Stat Phys 57, 1–39 (1989). https://doi.org/10.1007/BF01023632
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DOI: https://doi.org/10.1007/BF01023632