Heisenberg antiferromagnet on the square lattice for S>=1

Theoretical predictions of a semiclassical method - the pure-quantum self-consistent harmonic approximation - for the correlation length and staggered susceptibility of the Heisenberg antiferromagnet on the square lattice (2DQHAF) agree very well with recent quantum Monte Carlo data for S=1, as well as with experimental data for the S=5/2 compounds Rb2MnF4 and KFeF4. The theory is parameter-free and can be used to estimate the exchange coupling: for KFeF4 we find J=2.33 +- 0.33 meV, matching with previous determinations. On this basis, the adequacy of the quantum nonlinear sigma model approach in describing the 2DQHAF when S>=1 is discussed.