Ground-state energy of Heisenberg antiferromagnet for spins s=1/2 and s=1 in d=1 and 2 dimensions

A simple real-space renormalization method yields the ground-state energy of the Heisenberg antiferromagnet. We find the ground-state energy per spin for s=1/2 (-0.4438 in ID , -0.6723 in 2D ) and s = 1 (-1.388 in ID and -1.907 in 2D) to three-figure accuracy, using properties of relatively small odd-numbered clusters. Our results provide reasonable proof for long-range order in the ground state of the s = 1/2 Heisenberg antiferromagnet in 2D .