Superintegrable chiral Potts model: Thermodynamic properties, an inverse model, and a simple associated Hamiltonian

The partition function of the N-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 tension. The critical exponents are α = 1 - 2/N, μhor = νhor = 2/N, and μvert = 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 of N by N matrices. Inverting this matrix gives a related solvable model which is a generalization of the free-fermion model. The associated Hamiltonian has a very simple form, suggesting that may be a more direct algebraic method (perhaps a generalized Clifford algebra) for obtaining its eigenvalues