On the relation between Phi((1,2)) and Phi((1,5)) perturbed minimal models and unitarity

We consider the RSOS S-matrices of the Phi((1,5)) perturbed minimal models which have recently been found in a companion paper. These S-matrices have some interesting properties, in particular, unitarity may be broken in a stronger sense than seen before, while one of the three classes of Phi((1,5)) perturbations (to be described) shares the same thermodynamic Bethe ansatz as a related Phi((1,2)) perturbation. We test these new S-matrices by the standard Truncated Conformal Space method, and further observe that in some cases the BA equations for two particle energy levels may be continued to complex rapidity to describe (a) single particle excitations and (b) complex eigenvalues of the Hamiltonian corresponding to non-unitary S-matrix elements. We make some comments on identities between characters in the two related models following from the fact that the two perturbed theories share the same breather sector. (C) 1997 Elsevier Science B.V.