In the first talk we discussed some models that can be attacked via the trace map as well as some model-independent result. In this talk we shall apply our model-independent results to some specific models (Jacobi operators, CMV matrices, quantum and classical Ising models) and derive answers to questions that until quite recently were open. We will also present a connection between CMV matrices and Ising models. We shall state also some open problems and propose some routes for further development.