We consider a resonating-valence-bond state as a variational estimate for the ground state of a Heisenberg antiferromagnet. We derive an expression for the normalization of this wave function, which is a superposition of a very large number of singlet pair states, which we then use to show that the singularities, correlations, and low-lying excitations of this quantum system can be calculated from the partition function of a related dimerlike classical statistical mechanics problem. Possible calculational schemes are discussed.