Cube cluster approximation for the spin glass in the simple cubic lattice

The spin glass in the random-bond Ising model on a simple cubic lattice is considered. A simple method to calculate the partial trace of the density matrices of a fairly large cluster by use of the REDUCE system is presented. The phase diagram showing the paramagnetic, ferromagnetic, antiferromagnetic and spin glass states is obtained for the ±J model on the simple cubic lattice by the cube cluster approximation. The spin glass transition temperature is obtained with the inclusion of enough frustration of the cube clusters, and kTg/J=0.9850 for p (the concentration of the +J bond) = 1/2.