51 citations · 251 across the 16 of their papers we have counts for
16 papers
Critical exponents of the two dimensional Coulomb gas at the Berezinskii-Kosterlitz-Thouless transition
Pierluigi Falco
The two dimensional Coulomb gas is the prototypical model of statistical mechanics displaying a special kind of phase transition, named after Berezinskii, Kosterlitz and Thouless.…
Correlation Critical Exponents for the Six-Vertex Model
Pierluigi Falco
The six-vertex model on a square lattice is "exactly solvable" because an exact formula for the free energy can be obtained by Bethe Ansatz. However, exact formulas for the correla…
Universality of one-dimensional Fermi systems, II. The Luttinger liquid structure
Giuseppe Benfatto, Pierluigi Falco, Vieri Mastropietro
We complete the proof started in "Universality of one-dimensional Fermi systems, I." of the universal Luttinger liquid relations for a general model of spinning fermions on a latti…
Universality of one-dimensional Fermi systems, I. Response functions and critical exponents
Giuseppe Benfatto, Pierluigi Falco, Vieri Mastropietro
The critical behavior of one-dimensional interacting Fermi systems is expected to display universality features, called Luttinger liquid behavior. Critical exponents and certain th…
Interacting Fermions Picture for Dimer Models
Pierluigi Falco
Recent numerical results on classical dimers with weak aligning interactions have been theoretically justified via a Coulomb Gas representation of the height random variable. Here…
Two-dimensional Quantum Field Models (with applications to Statistical Mechanics)
Pierluigi Falco
Two dimensional toy models display, in a gentler setting, manysalient aspects of Quantum Field Theory. Here I discuss a concrete two dimensional case, the Thirring model, which ill…
Universal Luttinger Liquid Relations in the 1D Hubbard Model
Giuseppe Benfatto, Pierluigi Falco, Vieri Mastropietro
We study the 1D extended Hubbard model with a weak repulsive short-range interaction in the non-half-filled band case, using non-perturbative Renormalization Group methods and Ward…
Kosterlitz-Thouless Transition Line for the Two Dimensional Coulomb Gas
Pierluigi Falco
With a rigorous renormalization group approach, we study the pressure of the two dimensional Coulomb Gas along a small piece of the Kosterlitz-Thouless transition line, i.e. the bo…
Vector and Axial anomaly in the Thirring-Wess model
Pierluigi Falco
We study the 2D Vector Meson model introduced by Thirring and Wess, that is to say the Schwinger model with massive photon and massless fermion. We prove, with a renormalization gr…
Universal Relations for Non Solvable Statistical Models
G. Benfatto, P. Falco, V. Mastropietro
We present the first rigorous derivation of a number of universal relations for a class of models with continuously varying indices (among which are interacting planar Ising models…
Extended scaling relations for planar lattice models
G. Benfatto, P. Falco, V. Mastropietro
It is widely believed that the critical properties of several planar lattice models, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective Quantum F…
Massless Sine-Gordon and Massive Thirring Models: proof of the Coleman's equivalence
G. Benfatto, P. Falco, V. Mastropietro
We prove the Coleman's conjecture on the equivalence between the massless Sine-Gordon model with finite volume interaction and the Thirring model with a finite volume mass term.
Renormalization Group and Asymptotic Spin--Charge separation for Chiral Luttinger liquids
P. Falco, V. Mastropietro
The phenomenon of Spin-Charge separation in non-Fermi liquids is well understood only in certain solvable d=1 fermionic systems. In this paper we furnish the first example of asymp…
Rigorous construction of the Thirring model: Ward-Takahashi Identities, Schwinger-Dyson Equations and New Anomalies
Pierluigi Falco
We provide a rigorous construction of the Schwinger functions for the massive and massless Thirring models. We use the renormalization group approach, controlling its flow through…
Functional Integral Construction of the Thirring model: axioms verification and massless limit
G. Benfatto, P. Falco, V. Mastropietro
We construct a QFT for the Thirring model for any value of the mass in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are re…
Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus
F. Bonetto, P. Falco, A. Giuliani
We consider the "thermodynamic limit"of a d-dimensional lattice of hyperbolic dynamical systems on the 2-torus, interacting via weak and nearest neighbor coupling. We prove that th…