Localisation and density of spin wave states in a dilute two-dimensional Heisenberg ferromagnet

Abstract

The authors calculate the density of spin wave states, and their localisation properties, on the infinite percolating cluster of a randomly bond-dilute, two-dimensional Heisenberg ferromagnet. The results, in contrast to those of Fujiwara (1977, 1978), are consistent with the localisation of all states for p<1, and demonstrate strong localisation of states for p<or=0.7. They discuss the states at E approximately=0, p approximately=1 in terms of the self-energy, and find agreement with the earlier work of Kirkpatrick (1973). The most common Kirkpatrick-Eggarter special states for this system are identified and enumerated. The states at p=pc=0.5 are considered in detail, and they show how various features of the density of states are related to the properties of the eigenstates.