Mauro Melchiades Doria

A factorizable S-matrix given the free energy of one of the six-vertex models is obtained. This and the sine-Gordon theory are the only possible cases of S-matrices for the interaction of a particle and its antiparticle such that C, P and T are symmetries of the scattering amplitudes and charge is conserved. A third S-matrix can be defined when the coupling constant value of these two S-matrices go to infinity. It corresponds to the (DELTA) = -1 six-vertex model in Lieb and Wu’s classification.

A factorizable S-matrix describing the scattering of a Majorana fermion and a scalar boson is obtained. We use it compute the free energy per site of an asymmetric eight-vertex model, which happens to be a special case of the free-fermion models, solved by Fan and Wu using dimers. For a particular value of the parameters, this S-matrix acquires supersymmetry and is essentially the one previously found by Shankar and Witten. Tunning the coupling constants and the rapidity now at an other value give the free energy of the Ising Model.

A factorizable S-matrix for the scattering of two species of Majorana fermions and invariant under their exchange is derived by using Baxter’s eight-vertex solution of the factorization equations. A field theory model able to yield the scattering amplitudes of this S-matrix is proposed.

Factorizable supersymmetric S-matrices for particles with vanishing central charge are shown to decouple into the product of two S-matrices. One only carries the isospin content and the other is the S-matrix of the supersymmetric sine-Gordon model. This decomposition rule should give the S-matrix for the particles of the supersymmetric and completely integrable generalizations of many models, like the Toda chain, for instance.

An addition formula containing all the addition relations for the theta functions with characteristic proportional to 1/N, N integer, is derived. These theta functions provide the solution of the factorization equations with symmetry Z(,N) x Z(,N) as proven by Belavin. The Baxter model corresponds to N = 2; this addition theorem contains required information to compute the free energy of the lattice models based on this symmetry Z(,N) x Z(,N).