Dipolar Interactions at Ferromagnetic Critical Points

Abstract

The critical behavior for $T>\mathrm{}{T}_c$ and $H=0\mathrm{}$ of ferromagnets with both isotropic exchange coupling and dipolar interactions is studied by exact renormalization-group techniques in $d=4-\epsilon$ dimensions ($\epsilon >0\mathrm{}$) with ($n=d$)-component spins. A crossover from short-range isotropic (Heisenberg) to characteristic dipolar behavior occurs. The asymptotic spin-spin correlation function develops a factor ${\delta }_{\alpha \beta }-\frac{q^{\alpha }{q}^{\beta }}{q^2}$ which suppresses longitudinal fluctuations. Experiments on EuO and EuS are considered.