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

Abstract

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 models of two-component spins coupled by long range interactions. This failure occurs when accidental soft modes are provided by harmonic approximation owing to accidental infinite degeneracy of the ground state configuration. Indeed simple spin wave theory gives no long range order both for isotropic long range antiferromagnetic interaction decaying as 1/r3 and for dipolar interaction. On the contrary renormalized spin wave theory replaces accidental soft modes by temperature dependent gaps, so providing no long range order in the former case and long range order in the latter case in agreement with Monte Carlo simulation.