Critical behavior of N-component spin systems with random impurities in cubic-anisotropy crystalline material

Static and dynamic critical behavior of N-component spin systems with cubic anisotropy and with quenched random impurities are studied in the limit εd→0+ of the impurity system whose impurities are strongly correlated in εd dimensions while they are randomly distributed in the remaining d − εd dimensions. By means of the renormalization-group approach, the stability of the fixed points, the flow of the interactions and the critical exponents are evaluated up to two-loop order. The behavior of the first order phase transition to appear is also studied.