Critical Behavior of Magnets with Dipolar Interactions. IV. Anisotropy

Abstract

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 $n=d=4-\epsilon >m>\mathrm{}1\mathrm{}$ components), the critical exponent $\nu$ is $2\nu =1+\frac{\left(\frac{1}{2}\right){\mathrm{}(m+2\mathrm{})\mathrm{}}^2\epsilon }{(m^2+10m+12)}+O\left({\epsilon }^2\right)$ [to be compared with $2\nu =1+\frac{\left(\frac{1}{2}\right)(m+2\mathrm{})\mathrm{}\epsilon }{\mathrm{}(m+8\mathrm{})\mathrm{}}+O\left({\epsilon }^2\right)$ for the pure-exchange case]. For antiferromagnets, the pure-exchange exponents apply.