Effective-field theory of spin glasses and the coherent-anomaly method. I

Abstract

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 ~,= 5.2(1) for Ts~ =0, which agrees well with the data by some other authors. As for the threedimensional +J model, the present tentative analysis gives Tsa = 1.2(1)(J/kB) and 7,= 4(1), but more extensive calculations are needed.