Thanks to integrable quantum field theories, there has been in recent years new understanding on a large number of models of interest in statistical mechanics or in condensed matter physics, e.g. Ising model in a magnetic field or Sine-Gordon model. Integrability has permitted to determine, for instance, the exact spectrum of many systems, the explicit determination of the correlation functions of their order parameters, as well as their thermodynamical properties. In the seminar there will be discussed two methods which permit to extend this analysis also to non-integrable models: the first one is based on the Form Factor Perturbation Theory while the second is based on semi-classical techniques. Both approaches will be illustrated by studying in details the non-integrable features of a particular significant example, the Double Sine-Gordon model. This model is important in many physical contexts, as in the discussion of quantum spin chains or in the analysis of the O(3) sigma model with topological term.

SISSA, Italie