MEAN FIELD-THEORY OF DILUTE SPIN-GLASSES WITH POWER-LAW INTERACTIONS

We argue that in order to describe dilute dipolar or RKKY spin-glasses, a broad distribution of couplings (i.e. decaying as a power law) is more appropriate than the traditional Gaussian distribution. We present a mean-field 'replica symmetric' theory for this problem. We find that the spin-glass transition is of a different nature than the one occurring in the SK model, and resembles a percolation transition. The de Almeida-Thouless temperature is lower than the spin-glass transition temperature. The degree of 'replica symmetry breaking', measured by the absolute value of the negative entropy, is found to be smaller than in the SK model and non-monotonic with temperature. Some experimental consequences are briefly addressed.