New field theoretical method for spin 1/2

Abstract

A new field theoretic method for spin 12, for which the propagator and the finite temperature perturbation theory rules have been recently derived, is analysed in some detail. This propagator can be diagonalised using a spherical basis with the third axis along the magnetic field direction. The diagrammatic representation of the spherical spin components is given. As an illustration of this method, we derive some single spin quantities and the usual equation of state and spin wave spectrum of the spin 12 Heisenberg model, using the Hartree-Fock and the random phase approximations. We show how the field theoretic renormalisation group techniques can be applied to renormalise the different quantities of interest and to derive renormalisation group equations. As an example of their application, we consider the commutative and noncommunicative models of two-level systems in metallic glasses.