What is the lowest spin for which Néel order is possible in the d=2 Heisenberg model?

An important quantity for quantum antiferromagnets in d=2 is S_c, the lowest value of spin for which Néel order is possible in the ground state of the Heisenberg Hamiltonian. By using the first three known terms of the 1/S expansion for the ground state magnetization M, together with the fact that M must vanish as (SS_c)^β, where β is the magnetization exponent of the n=3 classical Heisenberg model in d=3, we estimate that S_c=0.38. Our Padé analysis also estimates that for S= 1 2, M=0.54S. If the Padé answer is the full story, the next term in the 1/S expansion will have a coefficient ≈ - 2 3(0.2)³.