  We consider classical and quantum integrable sigma models and their relations
with the solutions of renormalization group equations. We say that an
integrable sigma model possesses the "nice" duality property if the dual
quantum field theory has the weak coupling region. As an example, we consider
the deformed $CP(n-1)$ sigma model with additional quantum degrees of freedom.
We formulate the dual integrable field theory and use perturbed conformal field
theory, perturbation theory, $S$-matrix, Bethe Ansatz and renormalization group
methods to show that this field theory has the "nice" duality property. We
consider also an alternative approach to the analysis of sigma models on the
deformed symmetric spaces, based on the perturbed rational conformal field
theories.
