Critical behavior of magnets with dipolar interactions. IV. Anisotropy

Renormalization-group recursion formulas for magnets with dipolar interactions, derived in previous papers, are generalized to include the case of anisotropic exchange and dipolar forces. For a ferromagnet with a dominant m isotropy (the original spins having n=d=4-ε>m>1 components), the critical exponent ν is 2ν=1+(12)(m+2)2ε(m2+10m+12)+O (ε2) [to be compared with 2ν=1+(12)(m+2)ε(m+8)+O (ε2) for the pure-exchange case]. For antiferromagnets, the pure-exchange exponents apply.