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

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,μhor=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.