Quantum Monte Carlo calculation of the long-range order in the Heisenberg antiferromagnet.

The forward-walking Green's function Monte Carlo (GFMC) method is used to compute the staggered magnetization m y in the two-dimensional, spin-1=2 Heisenberg Antifer-romagnet on L L square lattices, up to L = 12. Unlike previous GFMC calculations, the method is unbiased and projects out the exact, rotationally invariant groundstate. These calculations provide connrmation of the existence of long-range antiferromagnetic order in the groundstate. A known relationship between m y and the leading nite size correction, coupled with high precision groundstate energy calculations, is used to reduce the error in extrapolating to the thermodynamic limit. The data extrapolate to m y = :3075 :0025, only slightly diierent from the spin-wave theory result :3034. Several perfect singlet trial wavefunctions used to reduce the statistical error are discussed. A possible explanation as to why exact diagonalization extrapolations tend to yield low values of m y is presented.