The first-order nature of the antiferromagnetic transitions in Cr, Eu, U${\mathrm{O}}_2$, and MnO can be explained by noting that the corresponding Landau-Ginzburg-Wilson Hamiltonians possess no stable fixed points in $4-\epsilon$ dimensions. We predict that all fcc type-I ($\overrightarrow{\mathrm{m}}\perp \overrightarrow{\mathrm{k}}$), type-II, and type-III ($\overrightarrow{\mathrm{m}}\perp \mathrm{}\left[100\right]\mathrm{}$, $\overrightarrow{\mathrm{k}}=\left[\frac{1}{2}01\right]$) antiferromagnetic transitions are first order.

• Received 13 October 1975

DOI:https://doi.org/10.1103/PhysRevLett.36.52