By means of the renormalisation-group approach, static and dynamic critical behaviours are studied for the XY spin system with cubic anisotropy and with quenched random nonmagnetic impurities. The stability of the quenched-random-impurity fixed point in d ( identical to 4- epsilon ) dimensions, the flow diagram of the interactions and the critical exponents are investigated, within the two-loop approximation, in terms of the epsilon 1/2 expansion. It is shown that the transition that appears is a first-order transition.
We study the static and dynamic critical behavior of N-component spin systems in crystals with cubic anisotropy in the presence of extended defects, namely ${\ensuremath{\epsilon}}_{d}$-dimensionally connected defects distributed randomly in d-${\ensuremath{\epsilon}}_{d}$ dimensions. These defects make the systems coordinate anisotropic. As a result of the presence of the cubic anisotropy and the coordinate anisotropy, various new types of critical behavior appear, e.g., an ${\ensuremath{\epsilon}}^{1/2}$ (\ensuremath{\epsilon}\ensuremath{\equiv}4-d) expansion for extended-defect XY systems, spiral trajectories, and oscillatory critical behavior for extended-defect systems, first-order phase transitions for extended-defect N-component systems with 2\ensuremath{\le}N<4 near the stability boundary of the free energy, and so on. The first two types of behavior will be investigated in detail.
The critical behavior at the special surface transition and crossover bevavior from special to ordinary surface transition in semi-infinite n-component anisotropic cubic models are investigated by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation. The crossover behavior for random semi-infinite Ising-like system, which is the nontrivial particular case of the cubic model in the limit
n→0, is also investigated. The numerical estimates of the resulting two-loop series expansions for the critical exponents of the special surface transition, surface crossover critical exponent
Φ and the surface critical exponents of the layer,
α1, and local specific heats,
α11, are computed by means of Pade and Pade-Borel resummation techniques. For
nnc the cubic fixed point is stable, where
nc is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behavior of semi-infinite systems with cubic anisotropy is characterized by new set of surface critical exponents for
n>nc.