Critical behavior of magnets with dipolar interactions. I. Renormalization group near four dimensions

The exact renormalization-group approach of Wilson is used to study the critical behavior for T>Tc, H=0, and small ε>0, of an isotropic ferromagnetic system in d=4-ε dimensions, with exchange and dipolar interactions between d-component spins. Normal isotropic Heisenberg behavior with 1γ12ν1-ε4 (to first order in ε) is retained for t=(TTc)-1GJad, where G=(g μB)22 measures the strength of the dipole-dipole interactions, J is the short-range exchange parameter, and a is the lattice spacing. When tφGJad, where φ1+ε4, crossover occurs to a characteristic dipolar behavior described by a new fixed point of the recursion relations. For tGJad one thus finds 1γ12ν1-9ε34 {and, for spins of n d components, 1γ12ν1-[(6n+3)2(6n+11)]ε, which agrees with spherical-model results when n→}. In the dipolar regime the spin-correlation function sqαs-qβ has a factor [δαβ-(qαqβq2)], which suppresses longitudinal spin fluctuations; the susceptibilities χαα display the expected demagnetization effects. It is found that dipolar anistropies derving from the lattice structure produce weak instabilities which should be hard to detect although their effects are not fully elucidated. Extensions of the results to nonzero magnetic fields, and to anistropic exchange interactions are indicated; the experimental situation is mentioned briefly.