Renormalization Group, hidden symmetries and approximate Ward identities in the XYZ model, II

An expansion based on renormalization group methods for the spin correlation function in the z direction of the Heisenberg-Ising XYZ chain with an external magnetic field directed as the z axis is derived. Moreover, by using the hidden symmetries of the model, we show that the running coupling constants are small, if the coupling in the z direction is small enough, that a critical index appearing in the correlation function is exactly vanishing (because of an approximate Ward identity) and other properties, so obtaining a rather detailed description of the XYZ correlation function.