  Second-order phase transitions appear as a divergence in one of the linear
response functions. For a system of correlated electrons, the relevant
divergent response can and does involve many-particle observables, most
famously the double occupancy. Generally, evaluating the linear response
function of many-particle observables requires a many-particle generalization
of the Bethe-Salpeter equation. However, here I show that the divergence of
linear response functions in dynamical mean-field theory is governed by a
two-particle Bethe-Salpeter equation, even for many-particle observables. The
reason for this is that the divergence at the second-order phase transition is
produced by the self-consistent feedback of the dynamical mean-field.
