On the Density-Density Critical Indices¶in Interacting Fermi Systems

The behaviour of correlation functions of d=1$ interacting fermionic systems is determined by a small number of critical indices. We prove that one of them is exactly zero. As a consequence, the behavior of the Fourier transform of the density-density correlation at zero momentum is qualitatively unaffected by the interaction, contrary to what happens at , if is the Fermi momentum. The result is obtained by implementing Ward identities in a Renormalization Group approach. Received: 12 November 2001 / Accepted: 25 February 2002?Published online: 2 October 2002     

Ward Identities and Vanishing of the Beta Function for d = 1 Interacting Fermi Systems

We give a self consistent and simplified proof of the (asymptotic) vanishing of the Beta function in d=1 interacting Fermi systems as a consequence of a few properties deduced from the exact solution of the Luttinger model. Moreover, since the vanishing of the Beta function is usually “proved” in the physical literature through heuristic arguments based on Ward identities, we briefly discuss here also the possibility of exploiting this idea in a rigorous approach, by using a suitable Dyson equation. We show that there are serious difficulties, related to the presence of corrections (for which we get careful bounds), which are usually neglected.     

Intermolecular proton transfer in solid phase: a rare example of crystal-to-crystal transformation from hydroxo- to oxo-bridged iron(III) molecule-based magnet

Intermolecular proton transfer in solid phase from the hydroxo bridge to a water molecule occurs in a new mu-hydroxo iron(III) compound of formula {EtNH3[Fe2(ox)2Cl2(mu-OH)].2H2O}n leading to a still crystalline compound in which the mu-oxo bridge replaces the mu-hydroxo one. Both three-dimensional compounds exhibit magnetic ordering at Tc ca. 70 K due to a spin canting.     

Periodic Solutions for Completely Resonant Nonlinear Wave Equations with Dirichlet Boundary Conditions

We consider the nonlinear string equation with Dirichlet boundary conditions u_tt–u_xx=(u), with (u)=u³+O(u⁵) odd and analytic, 0, and we construct small amplitude periodic solutions with frequency for a large Lebesgue measure set of close to 1. This extends previous results where only a zero-measure set of frequencies could be treated (the ones for which no small divisors appear). The proof is based on combining the Lyapunov-Schmidt decomposition, which leads to two separate sets of equations dealing with the resonant and non-resonant Fourier components, respectively the Q and the P equations, with resummation techniques of divergent powers series, allowing us to control the small divisors problem. The main difficulty with respect to the nonlinear wave equations u_tt–u_xx+Mu=(u), M0, is that not only the P equation but also the Q equation is infinite-dimensional.     

Massless Sine-Gordon and Massive Thirring Models: Proof of Coleman’s Equivalence

We prove 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.     

Low Temperature Analysis of Two-Dimensional Fermi Systems with Symmetric Fermi Surface

We prove the convergence of the perturbative expansion, based on Renormalization Group, of the two point Schwinger function of a system of weakly interacting fermions in d = 2, with symmetric Fermi surface and up to exponentially small temperatures, close to the expected onset of superconductivity.     

Rigorous Proof of Luttinger Liquid Behavior in the 1d Hubbard Model

We give the first rigorous (non perturbative) proof of Luttinger liquid behavior in the one dimensional Hubbard model, for small repulsive interaction and values of the density different from half filling. The analysis is based on the combination of multiscale analysis with Ward identities based on a hidden and approximate local chiral gauge invariance. No use is done of exact solutions or special integrability properties of the Hubbard model, and the results can be in fact easily generalized to include non local interactions, magnetic fields or interaction with external potentials     

Universality Relations in Non-solvable Quantum Spin Chains

We prove the exact relations between the critical exponents and the susceptibility, implied by the Haldane Luttinger liquid conjecture, for a generic lattice fermionic model or a quantum spin chain with short range weak interaction. The validity of such relations was only checked in some special solvable models, but there was up to now no proof of their validity in non-solvable models.     

Vanishing of Drude Weight in Interacting Fermions on $${\mathbb Z}^d$$ with Quasi-Periodic Disorder

Journal of Statistical Physics - We provide a very simple argument showing that the $$\Phi ^4_3$$ measure does have quartic exponential tails, as expected from its formal expression. This shows...