  Using renormalization group methods, we study the Heisenberg-Ising XYZ chain
in an external magnetic field directed as the z axis, in the case of small
coupling J_3 in the z direction. We study the asymptotic behaviour of the spin
space-time correlation function in the direction of the magnetic field and the
singularities of its Fourier transform.
  The work is organized in two parts. In the present paper an expansion for the
ground state energy and the effective potential is derived, which is convergent
if the running coupling constants are small enough. In the subsequent paper, by
using hidden symmetries of the model, we show that this condition is indeed
verified, if J_3 is small enough, and we derive an expansion for the spin
correlation function. We also prove, by means of an approximate Ward identity,
that a critical index, related with the asymptotic behaviour of the correlation
function, is exactly vanishing.
