Ground-state staggered magnetization of two-dimensional quantum Heisenberg antiferromagnets

The ground-state staggered magnetization of spin-S quantum Heisenberg antiferromagnets may be estimated in spin-wave theory (effectively a 1/S expansion) or by perturbation in $J_{\perp }$=$J_x$=$J_y$ away from the Ising ($J_{\perp }$=0, $J_z$>0) limit. The latter series in $J_{\perp }^2$ is poorly convergent for the square lattice and a naive summation of the available terms yields overestimates of the staggered magnetization. A new way of analyzing the perturbation series that should remove the slow convergence is proposed. The resulting ground-state staggered magnetization per spin for spin-1/2 is 0.313, while spin-wave theory yields 0.303, in units where the full, classical staggered magnetization is 0.500.