First-Order Transitions, Symmetry, and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ε</mml:mi></mml:math>Expansion

Abstract

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 $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions. We predict that all fcc type-I ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{m}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$), type-II, and type-III ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{m}}\ensuremath{\perp}[100]$, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}=[\frac{1}{2}01]$) antiferromagnetic transitions are first order.