  We consider the simplest bosonic-type S-matrix which is usually regarded as
unphysical due to the complex values of the finite volume ground state energy.
While a standard quantum field theory interpretation of such a scattering
theory is precluded, we argue that the physical situation described by this
S-matrix is of a massive Ising model perturbed by a particular set of
irrelevant operators. The presence of these operators drastically affects the
stability of the original vacuum of the massive Ising model and its ultraviolet
properties.
