Freezing temperature in dilute ising spin glasses with long-range interactions

The onset of spin-glass freezing in dilute Ising systems with long-range interactions is investigated with the use of numerical simulations. We show that taking pair correlations explicitly into account results in the renormalization of the interaction matrix and suppression of the density of localized states compared with conventional mean field theory. Application of the theory to the RKKY interaction in the dilute limit raises the question of the appropriate boundary eigenvalue of the effective interaction matrix that separates localized and extended states. We identify the onset of spin-glass freezing with the temperature T_g at which this boundary eigenvalue is equal to one. Numerical simulations reproduces the linear concentration dependence of T_g in the very dilute limit, in agreement with scaling relations, and show a significant improvement over the conventional mean-field theory in the value obtained for the freezing temperature.