Nonequilibrium critical behavior of model statistical systems and methods for the description of its features

This paper reviews features in critical behavior of far-from-equilibrium macroscopic systems and presents current methods of describing them by referring to some model statistical systems such as the three-dimensional Ising model and the two-dimensional $XY$ model. The paper examines the critical relaxation of homogeneous and structurally disordered systems subjected to abnormally strong fluctuation effects involved in ordering processes in solids at second-order phase transitions. Interest in such systems is due to the aging properties and fluctuation–dissipation theorem violations predicted for and observed in systems slowly evolving from a nonequilibrium initial state. It is shown that these features of nonequilibrium behavior show up in the magnetic properties of magnetic superstructures consisting of alternating nanoscale-thick magnetic and nonmagnetic layers and can be observed not only near the film's critical ferromagnetic ordering temperature $T_{\rm c}$, but also over the wide temperature range $T \le T_{\rm c}$.