Communications in Mathematical Physics

, Volume 330, Issue 1, pp 153–215 | Cite as

Universality of One-Dimensional Fermi Systems, I. Response Functions and Critical Exponents

  • G. Benfatto
  • P. Falco
  • V. MastropietroEmail author


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 other 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.


Critical Exponent Thermodynamic Limit Hubbard Model Renormalization Constant Density Correlation 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomeItaly
  2. 2.Department of MathematicsCalifornia State universityNorthridgeUSA
  3. 3.Diparimento di Matematica F.EnriquezUniversità di MilanoMilanItaly

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