We reconsider the results cocerning the extreme-quantum $S=1/2$ square-lattice Heisenberg antiferromagnet with frustrating diagonal couplings ($J_1-J_2$ model) drawn from a comparison with exact-diagonalization data. A combined approach using also some intrinsic features of the self-consistent spin-wave theory leads to the conclusion that the theory strongly overestimates the stabilizing role of quantum flutcuations in respect to the N\'{ e}el phase in the extreme-quantum case $S=1/2$. On the other hand, the analysis implies that the N\'{ e}el phase remains stable at least up to the limit $J_{ 2}/J_{ 1} = 0.49$ which is pretty larger than some previous estimates. In addition, it is argued that the spin-wave ansatz predicts the existence of a finite range ($J_{ 2}/J_{ 1}<0.323$ in the linear spin-wave theory) where the Marshall-Peierls sigh rule survives the frustrations.
Categories: cond-mat
