Metallic spin-glasses beyond mean-field: An approach to the impurity-concentration dependence of the freezing temperature

A relation between the freezing temperature ($T^{}_{\rm g}$) and the exchange couplings ($J^{}_{ij}$) in metallic spin-glasses is derived, taking the spin-correlations ($G^{}_{ij}$) into account. This approach does not involve a disorder-average. The expansion of the correlations to first order in $J^{}_{ij}/T^{}_{\rm g}$ leads to the molecular-field result from Thouless-Anderson-Palmer. Employing the current theory of the spin-interaction in disordered metals, an equation for $T^{}_{\rm g}$ as a function of the concentration of impurities is obtained, which reproduces the available data from {\sl Au}Fe, {\sl Ag}Mn, and {\sl Cu}Mn alloys well.