Cluster mean-field model of the spin glasses: static properties

We propose and solve a phenomenological model of the spin-glass alloys in which dynamical clusters are the basic entity. Intracluster interactions are treated exactly while intercluster terms are handled using the Edwards-Anderson (EA) random-mean-field theory. Numerical computations for average cluster sizes containing $3\le N\le 6$ atoms of the static susceptibility and specific heat $C_m$ show that the former exhibits a sharp cusp at the freezing temperature $T_c$. For antiferromagnetic intracluster interactions the latter has a rounded maximum at a slightly higher temperature which reflects the intracluster exchange constant. These features, both of which could not be explained previously, are in semiquantitative accord with experiment. For ferromagnetic clusters, agreement between theory and experiment for $C_m$ is also satisfactory, but for somewhat larger ($N\ge 12$) cluster sizes. The present model represents a first step in going beyond a simple mean field theoretic approach; it can, thus, be inferred that the most important fluctuation corrections derive from strong correlations between nearby spins (clusters) to which correlations the specific heat is more sensitive than is the susceptibility.