The renormalization group in the theory of critical behavior

Abstract

The renormalization group approach to the theory of critical behavior is reviewed at an introductory level with emphasis on magnetic systems. Among recent results reported are the dependence of critical exponents above ${T}_{c}$ on dimensionality $d=4\ensuremath{-}\ensuremath{\epsilon}$; on the symmetry index or number of spin components, $n$; on the range and anisotropy of exchange couplings; and on dipolar interactions and lattice anisotropies, in ferro- and antiferromagnets. Calculations of the scaling functions for the equation of state and critical scattering are summarized.