Critical Behavior of Magnets with Dipolar Interactions. I. Renormalization Group near Four Dimensions
Abstract
The exact renormalization-group approach of Wilson is used to study the critical behavior for T>Tc, H=0, and small ɛ>0, of an isotropic ferromagnetic system in d=4-ɛ dimensions, with exchange and dipolar interactions between d-component spins. Normal isotropic Heisenberg behavior with 1γ~12ν~1-ɛ4 (to first order in ɛ) is retained for t=(TTc)-1<<GJad, 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 tφ~GJad, where φ~1+ɛ4, crossover occurs to a characteristic dipolar behavior described by a new fixed point of the recursion relations. For t<<GJad one thus finds 1γ~12ν~1-9ɛ34 {and, for spins of n d components, 1γ~12ν~1-[(6n+3)2(6n+11)]ɛ, which agrees with spherical-model results when n-->∞}. In the dipolar regime the spin-correlation function <sαqsβ-q> 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.
- Publication:
-
Physical Review B
- Pub Date:
- October 1973
- DOI:
- 10.1103/PhysRevB.8.3323
- Bibcode:
- 1973PhRvB...8.3323A