Phase transition in generalized inhomogeneous 'cubic' systems

In this paper we investigate peculiarities of phase transition in inhomogeneous systems. We consider a case of 'cubic' systems with anisotropy invariants in which the distribution of defects generates a small-world property. We define a fractional equation of motion for the order parameter for the systems with a small world property. Linearization of the equation of motion for the order parameter made it possible to define a non-linear dispersion law. A renormalization group analysis of phase transitions in the generalized inhomogeneous 'cubic' systems is presented. We discuss the dependence of critical behavior on the nonextensivity parameter of the system.