  The properties of a phase with large correlation length can be strongly
influenced by the underlying normal phase. We illustrate this by studying the
half-filled two-dimensional Hubbard model using cellular dynamical mean-field
theory with continuous-time quantum Monte Carlo. Sharp crossovers in the
mechanism that favors antiferromagnetic correlations and in the corresponding
local density of states are observed. These crossovers occur at values of the
interaction strength $U$ and temperature $T$ that are controlled by the
underlying normal-state Mott transition.
