  We report a neutron scattering study of the instantaneous spin correlations
in the two-dimensional spin S=5/2 square-lattice Heisenberg antiferromagnet
Rb_2MnF_4. The measured correlation lengths are quantitatively described, with
no adjustable parameters, by high-temperature series expansion results and by a
theory based on the quantum self-consistent harmonic approximation. Conversely,
we find that the data, which cover the range from about 1 to 50 lattice
constants, are outside of the regime corresponding to renormalized classical
behavior of the quantum non-linear sigma model. In addition, we observe a
crossover from Heisenberg to Ising critical behavior near the Neel temperature;
this crossover is well described by a mean-field model with no adjustable
parameters.
