Spin-rotation invariance and the structure of correlation functions in magnetic systems

We analyze, in the framework of the functional approach to statistical mechanics, general properties of correlation functions in ordered magnetic systems. The aim of this paper is to investigate what consequences can be derived from the requirement of invariance of the theory under local infinitesimal spin rotation. The extension of the method that we introduce, to include anisotropic Hamiltonians, is discussed, and the case of the anisotropy described by an internal field is worked out. Our main results are a set of generalized Ward identities, a microscopic definition of the stiffness constant as a static limit of a local response function, and an exact asymptotic expression for the correlation functions of interest, for zero temperature and small wave length and frequency. Modifications to the hydrodynamic expression for correlation functions in the case where anisotropy is present are also discussed.