Title: Magnetic Correlations in the Two-dimensional Repulsive Fermi Hubbard Model,
Abstract: The repulsive Fermi Hubbard model on the square lattice has a rich phase
diagram near half-filling (corresponding to the particle density per lattice
site $n=1$): for $n=1$ the ground state is an antiferromagnetic insulator, at
$0.6 < n \lesssim 0.8$, it is a $d_{x^2-y^2}$-wave superfluid (at least for
moderately strong interactions $U \lesssim 4t$ in terms of the hopping $t$),
and the region $1-n \ll 1$ is most likely subject to phase separation. Much of
this physics is preempted at finite temperatures and to an extent driven by
strong magnetic fluctuations, their quantitative characteristics and how they
change with the doping level being much less understood. Experiments on
ultra-cold atoms have recently gained access to this interesting fluctuation
regime, which is now under extensive investigation. In this work we employ a
self-consistent skeleton diagrammatic approach to quantify the characteristic
temperature scale $T_{M}(n)$ for the onset of magnetic fluctuations with a
large correlation length and identify their nature. Our results suggest that
the strongest fluctuations---and hence highest $T_{M}$ and easiest experimental
access to this regime---are observed at $U/t \approx 4-6$.