  In this paper, we revisit the antiferromagnetic (AF) phase diagram of the
single-band three-dimensional half-filled Hubbard model on a simple cubic
lattice studied within the dynamical mean field theory (DMFT). Although this
problem has been investigated extensively in the literature, a comprehensive
understanding of the impact of the different one- and, in particular,
two-particle local correlation functions of DMFT on the AF transition
temperature is still missing. We have, hence, performed a fluctuation analysis
of $T_N$ with respect to different local bosonic fluctuations (charge, spin,
particle-particle) contained in the two-particle vertex of DMFT. Our results
indicate that, beyond weak coupling, the screening of the DMFT vertex by local
fluctuations leads to an enhancement of $T_N$ with respect to a random phase
approximation (RPA) like calculation where this vertex is replaced by the bare
interaction. The overall suppression of $T_N$ in DMFT with respect to RPA is
then solely due to the incoherence introduced by the DMFT self-energy in the
one-particle Green's functions. This illustrates the Janus-faced role of the
local moment formation in the DMFT solution of the Hubbard model, which leads
to completely opposite effects in the one- and two-particle correlation
functions.
