Spin-glass ordering temperature beyond its mean-field value

A new method of evaluating the spin-glass ordering temperature beyond its mean-field value is given. The method is applied to a random-bond spin-glass system with $P\left(J_{\mathrm{ij}}\right)=P(-J_{\mathrm{ij}})$ and a dilute simple-cubic (sc) spin-glass alloy. An estimate of the spin-glass ordering temperature in the random-bond sc system is obtained. The critical percolation concentration of a dilute sc spin-glass alloy is estimated. The spin-glass ordering temperature in a dilute sc spin-glass alloy at first expresses an anomalous increase for dilution of magnetic atoms, which is interpreted as the release from the "frustration" of spin orientations which existed in a perfect sc spin-glass lattice. A preliminary report of this paper is published in Prog. Theor. Phys. 65, No. 2 (1981).