  The spin-fermion (SF) model postulates that the dominant coupling between
low-energy fermions in near critical metals is mediated by collective spin
fluctuations (paramagnons) peaked at the N\'{e}el wave vector, ${\bf Q}_N$,
connecting hot spots on opposite sides of the Fermi surface. It has been argued
that strong correlations at hot spots lead to a Fermi surface deformation (FSD)
featuring flat regions and increased nesting. This conjecture was confirmed in
the perturbative self-consistent calculations when the paramagnon propagator
dependence on momentum deviation from ${\bf Q}_N$ is given by $\chi^{-1}
\propto |\Delta q|$. Using diagrammatic Monte Carlo (diagMC) technique we show
that such a dependence holds only at temperatures orders of magnitude smaller
than any other energy scale in the problem, indicating that a different
mechanism may be at play. Instead, we find that a $\chi^{-1} \propto |\Delta
q|^{2}$ dependence yields a robust finite-$T$ scenario for achieving FSD. To
link phenomenological and microscopic descriptions, we applied the connected
determinant diagMC method to the $(t-t')$ Hubbard model and found that in this
case: (i) the FSD is not very pronounced, and, instead, it is the lines of
zeros of the renormalized dispersion relation that deform towards nesting; (ii)
this phenomenon appears at large $U/t>5.5$ before the formation of electron and
hole pockets; (iii) the static spin susceptibility is well described by
$\chi^{-1} \propto |\Delta q|^{2}$. Flat FS regions yield a non-trivial
scenario for realizing a non-Fermi liquid state.
