  We study the impact of the fermionic self-energy on one-loop functional
renormalization group flows of the two-dimensional $t$-$t'$ Hubbard model, with
emphasis on electronic densities away from van Hove filling. In the presence of
antiferromagnetic hot spots, antiferromagnetic fluctuations lead to a
flattening of the Fermi surface, shift magnetic phase boundaries and
significantly enhance critical scales. We trace back this effect to the
presence of a magnetic first order transition. For some parameters, the first
order character of the latter is reduced by self-energy effects. For reliably
determining phase diagrams, the fermionic self-energy should thus be taken into
account in functional renormalization group studies if scattering between hot
spots is important.
