Ground-State Energy of Heisenberg Antiferromagnet for Spins $s=\frac{1}{2}$ and $s=1\mathrm{}$ in $d=1\mathrm{} \mathrm{and} 2$ 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 $s=\frac{1}{2}$ (-0.4438 in 1D, -0.6723 in 2D) and $s=1\mathrm{}$ (-1.388 in 1D 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 $s=\frac{1}{2}$ Heisenberg antiferromagnet in 2D.