Critical behavior of the random uniaxial anisotropy model

Abstract

The critical behav or of an isotropic ferromagnet with random uniaxial anisotropy is studied to the first order in $\epsilon =6-d$. Even though the fourth-order coefficients are irrelevant for $d>\mathrm{}4\mathrm{}$, and the exponents are all given by their mean-field values, the longitudinal susceptibility for $T<\mathrm{}{T}_c$ is found to diverge on the coexistence curve for $d<~6$. Thus the upper critical dimension is $d_c=6\mathrm{}$ for this nodel.