Effective-Field Theory of Spin Glasses and the Coherent-Anomaly Method. I

A new cluster-effective-field theory of spin glasses is formulated. Basic formulas for the spin-glass transition point and the spin-glass susceptibility in the high-temperature phase are obtained. The present theory combined with the coherent-anomaly method is shown to be useful to estimate the true critical point and the nonclassical critical exponent of a spin-glass transition. Concerning the two-dimensional ±J model, we have γ_s = 5.2(1) for T_SG = 0, which agrees well with the data by some other authors. As for the three-dimensional ±J model, the present tentative analysis gives T_SG = 1.2(1)(J/k_B) and γ_s = 4(1), but more extensive calculations are needed.