Antiferromagnetic correlations of the resonating-valence-bond state

We consider a trial wave function for the two-dimensional spin-½ antiferromagnetic Heisenberg model (resonating-valence-bond state), which is a sum of all dimerizations. It is shown that the antiferromagnetic correlation length is bounded by that of a classical gas of interacting loops with $n=4\mathrm{}$ components. We argue that the range of the antiferromagnetic correlations is finite and triplet excitation has an energy gap.