**Authors:**
Giuseppe Benfatto, Pierluigi Falco, Vieri Mastropietro

**Title:** *
Universality of one-dimensional Fermi systems, I. Response functions and critical exponents
*

**Abstract: **
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.

**Keywords:**
1D Hubbard model, Luttinger liquid behavior, critical exponents,
renormalization group

Giuseppe Benfatto

Dipartimento di Matematica

Università di Roma Tor Vergata

V.le della Ricerca Scientifica 1, 00133 Roma - Italy

e-mail: benfatto AT mat DOT uniroma2 DOT it

Pierluigi Falco

Department of Mathematics

California State University, Northridge

e-mail: pierluigi DOT falco AT csun DOT edu

Vieri Mastropietro

Dipartimento di Matematica

Università di Milano

Via Saldini, 50, I-20133 Milano - ITALY

e-mail: Vieri DOT Mastropietro AT unimi DOT it