  We analyze the evolution of the effective potential and the particle spectrum
of two-parameter families of non-integrable quantum field theories. These
theories are defined by deformations of conformal minimal models M_m by using
the operators Phi_{1,3}, Phi_{1,2} and Phi_{2,1}. This study extends to all
minimal models the analysis previously done for the classes of universality of
the Ising, the Tricritical Ising and the RSOS models. We establish the symmetry
and the duality properties of the various models also identifying the limiting
theories that emerge when m goes to infinity.
