  The critical behavior of one-dimensional interacting Fermi systems is
expected to display universality features, called Luttinger liquid behavior.
Critical exponents and certain thermodynamic quantities are expected to be
related among each others by model-independent formulas. We establish such
relations, the proof of which has represented a challenging mathematical
problem, for a general model of spinning fermions on a one dimensional lattice;
interactions are short ranged and satisfy a positivity condition which makes
the model critical at zero temperature. Proofs are reported in two papers: in
the present one, we demonstrate that the zero temperature response functions in
the thermodynamic limit are Borel summable and have anomalous power-law decay
with multiplicative logarithmic corrections. Critical exponents are expressed
in terms of convergent expansions and depend on all the model details. All
results are valid for the special case of the Hubbard model.
