The renormalization-group method in the theory of phase transitions

The renormalization group for the statistical mechanics of a wave field is described. The hypothesis of scaling of correlations near an order-disorder phase-transition point is written in renormalization-group terms. The renormalization-group equations near a fixed point are investigated. The scaling dimensions (critical indices) of the principal quantities are found in the $\epsilon$-approximation. The stability of manycomponent systems and the question of asymptotic symmetry are investigated. The renormalization method is applied to the study of the dynamics of systems near a phase-transition point.