FM 2000-12 mp_arc #00-183
Authors: G. Benfatto, V. Mastropietro.
Title: Renormalization Group, hidden symmetries and approximate Ward
identities in the XYZ model, I.
Abstract:
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.
Key Words: Quantum Statistical Mechanics, Renormalization Group, Fermi
systems.