Site Disordered Spin Systems in the Gaussian Variational Approximation

We define a replica field theory describing finite dimensional site disordered spin systems by introducing the notion of grand canonical disorder, where the number of spins in the system is random but quenched. A general analysis of this field theory is made using the Gaussian variational or Hartree Fock method, and illustrated with several specific examples. Irrespective of the form of interaction between the spins this approximation predicts a spin glass phase. We discuss the replica symmetric phase at length, explicitly identifying the correlator that diverges at the spin glass transition. We also discuss the form of continuous replica symmetry breaking found just below the transition. Finally we show how an analysis of ferromagnetic ordering indicates a breakdown of the approximation.