ABSTRACT
This chapter presents a simplified version which, from the beginning, aims at an application of the method to systems of interacting spins. An alternative and, by far, simpler way to take into account some correlations is the Green’s function method which can treat the whole temperature range going from low-temperature phase up to the transition temperature. The random-phase approximation (RPA) is hierarchically higher than the mean-field theory in the sense that one operator in a three-operator product is replaced by its average value in the RPA while in the mean-field theory one operator in a two-operator product is replaced. In frustrated spin systems, the competition between different kinds of interaction can give rise to ground-state spin configurations which are not collinear. The incompatibility of some lattice geometries with antiferromagnetic interaction yields also non-collinear spin configurations as those in the antiferromagnetic triangular lattice, in the antiferromagnetic face-centered cubic lattice or hexagonalclose-packed lattice.
