Energy spectrum and critical exponents of the free parafermion ZN spin chain

Results are given for the ground state energy and excitation spectrum of a simple N-state Z(N) spin chain described by free parafermions. The model is non-Hermitian for N >= 3 with a real ground state energy and a complex excitation spectrum. Although having a simpler Hamiltonian than the superintegrable chiral Potts model, the model is seen to share some properties with it, e.g. the specific heat exponent alpha = 1 - 2/N and the anisotropic correlation length exponents nu(parallel to) = 1 and nu(perpendicular to) = 2/N.