Long range order in two-dimensional spin models with long range interactions

We show that simple spin wave theory does not provide a reliable indication of long range order or no long range order in two-dimensional square model s of two-component spins coupled by long range interactions. This failure o ccurs when accidental soft modes are provided by harmonic approximation owi ng to accidental infinite degeneracy of the ground state configuration. Ind eed simple spin wave theory gives no long range order both for isotropic lo ng range antiferromagnetic interaction decaying as 1/r(3) and for dipolar i nteraction. On the contrary renormalized spin wave theory replaces accident al soft modes by temperature dependent gaps, so providing no long range ord er in the former case and long range order in the latter case in agreement with Monte Carlo simulation. (C) 1999 American Institute of Physics. [S0021 -8979(99)41108-9].