Magnetic excitations on two-dimensional percolating clusters.

Abstract

We have carried out numerical studies of the exponent characterizing the distribution of low-energy magnon modes on the infinite percolating cluster of the two-dimensional, bond-dilute, nearest-neighbor Heisenberg antiferromagnet and the XY model. In the case of the antiferromagnet we obtain agreement with the predictions of scaling theory using the value of the transverse susceptibility exponent given by Kumar and Harris. The agreement with scaling theory is somewhat less satisfactory for the XY model, but may improve with larger arrays.