On scaling fields in ZN Ising models

We study the space of scaling fields in the ZN symmetric models with factorized scattering and propose the simplest algebraic relations between the form factors induced by the action of deformed parafermionic currents. The construction gives a new free field representation for form factors of perturbed Virasoro algebra primary fields, which are parafermionic algebra descendants. We find exact vacuum expectation values of physically important fields and study the correlation functions of order and disorder fields in the form factor and conformal field theories perturbation approaches.