Is Kaniadakis κ-generalized statistical mechanics general?

In this Letter we introduce some field-theoretic approach for computing the critical properties of systems undergoing continuous phase transitions governed by $\kappa$-generalized statistics, namely statistical field theory. particular, show, computations through analytic and simulation results, that Ising-like are not capable describing nonconventional real imperfect crystals, \emph{e. g.} manganites, as alternative generalized theory is, nonextensive theory, shown recently in literature. Although $\kappa$-Ising-like do depend on $\kappa$, show a few distinct do. Thus is general, \emph{i. e.} it fails to generalize behavior must be discarded one generalizing mechanics. For latter present physical interpretation furnishing general deformation $\kappa$-parameter.