  The spin and density correlation functions of the two-dimensional Hubbard
model at low electronic density $<n>$ are calculated in the ground state by
using the power method, and at finite temperatures by using the quantum Monte
Carlo technique. Both approaches produce similar results, which are in close
agreement with numerical and high temperature expansion results for the
two-dimensional ${\rm t-J}$ model. Using perturbative approximations, we show
that the examination of the density correlation function alone is not enough to
support recent claims in the literature that suggested spin and charge
separation in the low electronic density regime of the ${\rm t-J}$ model.
