  We have carried out a neutron scattering study of the instantaneous spin-spin
correlations in La2CuO4 (T_N = 325 K) over the temperature range 337 K to 824
K. Incident neutron energies varying from 14.7 meV to 115 meV have been
employed in order to guarantee that the energy integration is carried out
properly. The results so-obtained for the spin correlation length as a function
of temperature when expressed in reduced units agree quantitatively both with
previous results for the two dimensional (2D) tetragonal material Sr2CuO2Cl2
and with quantum Monte Carlo results for the nearest neighbor square lattice
S=1/2 Heisenberg model. All of the experimental and numerical results for the
correlation length are well described without any adjustable parameters by the
behavior predicted for the quantum non-linear sigma model in the low
temperature renormalized classical regime. The amplitude, on the other hand,
deviates subtly from the predicted low temperature behavior. These results are
discussed in the context of recent theory for the 2D quantum Heisenberg model.
