Crossover behavior of systems associated with extended-defect N-component systems in cubic anisotropic crystals

Abstract

Extended-defect N-component systems in cubic anisotropic crystals have fixed points of the Gaussian [G], Ising [P I], isotropic N-component [P N ] and cubic anisotropic N-component [P c N ] systems as regular (pure) systems, and those of the Ising [D I], isotropic N-component [D N ], cubic anisotropic XY [D c XY ] and cubic anisotropic N-component [D c N ] systems as extended-defect systems. Crossover behavior near these typical fixed point systems is studied by means of a renormalization-group (RG) approach and characteristic curve (CC) method. Crossover exponents of the systems and their behavior are calculated and illustrated to linear order in ϵ (≡ − d; d = dimension of space) and ≈ϵ (≡ϵ + ϵ d; ϵ d = dimension of space occupied by extended defects (impurities)).