Breakdown Of Mode-Mode Coupling Expansion For Commensurate Itinerant Antiferromagnetism In Two Dimensions

We consider the mode-mode coupling theory of two-dimensional commensurate itinerant antiferromagnets where Q spans the Fermi surface. It is shown that quantum (finite frequency) terms in the mode-mode coupling expansion are singular. The singularity is sufficiently strong that a mean-field-like quantum critical point does not exist.