Fluctuation effect and the spin-glass transition temperatures in the random-bond Ising models in the hexagonal, triangular, BCC and other lattices-unified description

Abstract

The cluster variational free energies of the random-bond Ising model are given in terms of effective fields and of effective interactions. The stationarity of the free energy gives the reducibilities between the one-body, two-body and cluster density matrices. From these reducibilities the uniform, staggered and spin-glass susceptibilities are obtained. A simple version of the above treatment is also presented which is called the cactus approximation. The phase diagrams of the binary (and ternary) mixtures of the ferromagnetic, antiferromagnetic (and non-magnetic) bonds in the triangular, hexagonal, and BCC lattices are obtained. The phase diagram of the triangular lattice is qualitatively similar to the FCC lattice and those of the hexagonal and BCC lattice to the square lattice. In particular the bond-diluted antiferromagnet in the triangular lattice is shown to have a spin-glass state.