Excitations in spin-glasses

Abstract

Starting from a ground state in which the spins have been frozen in random configurations we have analyzed the equations of motion for single-spin deviation excitations. The equations of motion involve two amplitudes at each site, just like an antiferromagnet. Making simple statistical assumptions about spin orientations in the ground state, we have analyzed the localization characteristics of these excitations. For a spin-glass model with short-ranged interactions, an explicit form of the localization function is derived. The local densities of states for spin deviation excitations have been calculated using a continued-fraction method for two models, namely (i) a small concentration of spins distributed randomly on a fcc lattice and interacting via a Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, (ii) spins on each lattice site but interacting via a random exchange integral having a Gaussian distribution. In each case we find a finite density of states at zero energy, and thus explain the low-temperature behavior of the specific heat. For the RKKY model, the density of states at zero energy is found to increase with decreasing concentration, and thus we are able to show the approximate concentration independence of the linear term of the specific heat. Our density-of-states curves agree fairly with those obtained in Monte Carlo calculations on finite numbers of spins.