Freezing of the extended states in mean field theory of dilute Ising spin glasses with long range interactions

Abstract

The onset of spin glass freezing in dilute systems with long range interactions is investigated within the framework of local mean field equations with the use of numerical simulations. The problem reduces to the diagonalization of a N × N random matrix, N being the number of spins in the simulation, whose elements depend on the spin-spin interaction and temperature. Application of the theory to the RKKY coupling in the dilute limit raises the question of the appropriate boundary eigenvalue of the interaction matrix separating localized and extended states. We identify the onset of spin glass freezing with the temperature at which this boundary eigenvalue is equal to one. Numerical simulations give a reasonable value of the freezing temperature for RKKY spin glasses and reproduce its linear concentration dependence in the very dilute limit.