Existence of Néel order at T=0 in the spin-1/2 antiferromagnetic Heisenberg model on a square lattice

It is known that if the ground state of the spin-1/2 antiferromagnetic Heisenberg model is not Néel ordered, the two-point function must satisfy an upper bound. In this paper, the spin-spin correlation function for the ground state is computed on a 32×32 square lattice using a projection Monte Carlo method. The correlation function at short distance (about four lattice spacing) violates this bound, which implies that the ground state must have long-ranged Néel order. I have also estimated the staggered magnetization to be ${\mathit{m}}^{+}$=0.304±0.004 in the thermodynamic limit.