Exact S-Matrices

The Ising model in a magnetic field is one of the most beautiful examples of an integrable model. This chapter presents its exact S-matrix and the exact spectrum of its excitations, which consist of eight particles of different masses. Similarly, it discusses the exact scattering theory behind the thermal deformation of the tricritical Ising model and the unusual features of the exact S-matrix of the non-unitary Yang–Lee model. Other examples are provided by O(n) invariant models, including the important Sine–Gordon model. It also discusses multiple poles, magnetic deformation, the E 8 Toda theory, bootstrap fusion rules, non-relativistic limits and quantum group symmetry of the Sine–Gordon model.