  The extension of the Lieb-Schultz-Mattis theorem to dimensions larger than
one is discussed. It is explained why the variational wave-function built by
the previous authors is of no help to prove the theorem in dimension larger
than one. The short range R.V.B. picture of Sutherland, Rokhsar and Kivelson,
Read and Chakraborty gives a strong support to the assertion that the theorem
is indeed valid in any dimension. Some illustrations of the general ideas are
displayed on exact spectra.
