Behavior of the mean spin on finite clusters in a model for the dilute Heisenberg antiferromagnet

We report a study of the mean spin on finite clusters with 2, 3, 4, 5 and 6 spins in a linearized spin wave model for the dilute antiferromagnet on a square lattice due to Thorpe and Alben. For 2 and 3 spin clusters, the results are compared to the exact results and to the exact solution of the linearized Green's function equations. We find that, as expected physically, the model treats this property of the small clusters in a manner which is neither self-consistent nor in accord with exact results. We discuss briefly how these results affect the validity of the use of the Thorpe and Alben model for other more global quantities.