Spin waves in a Mattis random magnet

It is shown that a random Heisenberg magnet characterized by H= 1 / 2 Sigma i J ij xi i xi j S i .S j , where J ij is a fixed function of the separation of sites i and j but the xi i are randomly +or-1, can sustain well defined long-wavelength spin waves with an antiferromagnetic-like linear dispersion.