Effective Sublattice Magnetization and Neel Temperature in Quantum Antiferromagnets

We present an analytic expression for the finite temperature effective sublattice magnetization which would be detected by inelastic neutron scattering experiments performed on a two-dimensional square-lattice quantum Heisenberg antiferromagnets with short range N'eel order. Our expression, which has no adjustable parameters, is able to reproduce both the qualitative behaviour of the phase diagram $M(T)xT$ and the experimental values of the N'eel temperature $T_N$ for either doped YBa${}_2$Cu${}_3$O${}_{6.15}$ and stoichiometric La${}_2$CuO${}_4$ compounds. Finally, we remark that by incorporating frustration and 3D effects as perturbations is sufficient to explain the deviation of the experimental data from our theoretical curves.