  Two-dimensional Hubbard lattices with two or three holes are investigated as
a function of $U$ in the large-$U$ limit. In the so-called Nagaoka limit
(one-hole system at infinite $U$), it is known that the Hubbard model exhibits
a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations
applied to periodic lattices up to 24 sites, we compute spin-spin correlation
functions as a function of increasing $U$. The correlation functions clearly
demonstrate the onset of ferromagnetic domains, centred on individual holes.
The overall total spin of the wavefunctions remain the lowest possible (0, or
$\frac{1}{2}$, depending on the number of holes). The ferromagnetic domains
appear at interaction strengths comparable to the critical interaction
strengths of the Nagaoka transition in finite systems with strictly one hole.
The existence of such ferromagnetic domains is the signature of Nagaoka physics
in Hubbard systems with a small (but greater than one) number of holes.
