Row transfer matrix spectra of cyclic solid-on-solid lattice models

The eigenvalue spectra of cyclic solid-on-solid (CSOS) row transfer matrices are studied. An equivalence is established between the inversion identity and the Bethe ansatz functional equations and these equations are solved in the thermodynamic limit by a Wiener-Hopf perturbation technique for the bands of leading excitations. The L-state CSOS model, with crossing parameter λ=πs/L, possesses a 2(L - s)-fold degenerate largest eigenvalue corresponding to the 2(L - s) coexisting phases. The expressions for the largest eigenvalue and free energy coincide with those of the eight-vertex model. The string excitations for 2 s < L and 2 s > L admit different classifications and are treated separately. The correlation length is calculated in both regimes, yielding the critical exponent v=L/2 s, in agreement with the scaling relations.