The superintegrable chiral potts model

Abstract

We extend recent work of Albertini et al. to the two-dimensional solvable N-state chiral Potts model corresponding to their “superintegrable” hamiltonian. We show that one can rigorously obtain a sub-set of the transfer matrix eigenvalues, and hence obtain the free energy, interfacial tension and correlation length in the usual way. This gives the values 1 − 2/ N, 2/ N, 1 for the corresponding critical exponents α, μ, v. These agree with the convincing but non-rigorous results of Albertini et al., and violate the hyperscaling relation dv = 2 − α.