  We analyze the infrared behavior of effective N-point interactions between
order parameter fluctuations for nematic and other quantum critical electron
systems with a scalar order parameter in two dimensions. The interactions
exhibit a singular momentum and energy dependence and thus cannot be
represented by local vertices. They diverge for all N greater or equal 4 in a
collinear static limit, where energy variables scale to zero faster than
momenta, and momenta become increasingly collinear. The degree of divergence is
not reduced by any cancellations and renders all N-point interactions marginal.
A truncation of the order parameter action at quartic or any other finite order
is therefore not justified. The same conclusion can be drawn for the effective
action describing fermions coupled to a U(1) gauge field in two dimensions.
