Constructive Renormalization Group: A conference in memory of Pierluigi Falco

Contribution List

17. Results and conjectures about the XY model

Thomas Spencer (IAS (USA))

09/06/2015, 09:30

In this review talk I will explain how Falco's work on the Coulomb gas is related to the 2D XY model at T_c. In 3D I will present some open problems at low temperature

12. The Coulomb system at the KT transition, part I

Roland Bauerschmidt (Harvard Univ. (USA))

09/06/2015, 11:00

In a recent paper http://arxiv.org/abs/1311.2237, Pierluigi Falco derived the detailed asymptotics of the correlation function of the critical Coulomb system in two dimensions at low density, as predicted by Berezinskii, Kosterlitz and Thouless. In this first of a two part lecture we will review this result and explain some key ideas in this remarkable achievement.

13. The Coulomb system at the KT transition, part II

David Brydges (British Columbia Univ. (Canada))

09/06/2015, 12:00

In a recent paper http://arxiv.org/abs/1311.2237, Pierluigi Falco derived the detailed asymptotics of the correlation function of the critical Coulomb system in two dimensions at low density, as predicted by Berezinskii, Kosterlitz and Thouless. In this second of a two part lecture we will review this result and explain some of key ideas in this remarkable achievement.

0. Renormalization group, Kondo effect and hierarchical models

Giovanni Gallavotti (INFN - Roma 1/ Rutgers University)

09/06/2015, 14:30

A manifestation of the Kondo effect is the non divergence at zero temperature of the susceptibility of an impurity magnetization to the action of a field. It is a quantum phenomenon not accessible to perturbation theory because it is essential that the interaction with the host lattice electrons is antiferromagnetic, no matter how small. Its theory in one dimension, due to Wilson, is...

11. The rigorous construction of the 1D Extended Hubbard model by RG techniques

Giuseppe Benfatto (Tor Vergata Univ.)

09/06/2015, 15:30

In the last twenty years, many people in Rome have studied various types of Fermion models, by applying rigorous RG techniques. One of these people was Pierluigi Falco and the paper I will speak about, written in collaboration with Vieri Mastropietro and myself, was his last one. The line of research on rigorous RG was open at the end of the 80's by Giovanni Gallavotti, who published...

15. Anomalies and universality in statistical mechanics

Prof. Vieri Mastropietro (Universita' di Roma Tor Vergata)

09/06/2015, 16:30

Around 2007 Pierluigi Falco sent me a two line mail writing something like "then we can prove the kadanoff relation $x_- x_+=1$". This was the end of a two year discussion between we two (which I will be recall in my seminar) on the renormalization/non renormalization of the anomalies in quantum field theory and its implications for universality in statistical mechanics; the complete...

2. Limit Theorems in Quantum Theory

Prof. Juerg Froehlich (ETH Zurich)

10/06/2015, 09:30

I present an outline of the theory of information acquisition in quantum mechanics. I discuss some relevant mathematical techniques from functional analysis and probability theory needed to develop this theory. In order to keep the presentation down to earth, I focus on the discussion of concrete examples of indirect and non-demolition measurements.

7. Universality of conductivity in interacting graphene

Marcello Porta (Zurich Univ.)

10/06/2015, 11:00

Graphene is a recently discovered material, which can be considered as the first realization of a two-dimensional crystal. Its unique physical properties elicited great interest in the condensed matter physics community, both from a theoretical and an experimental point of view. Remarkably, some interesting features of graphene can be understood from a mathematically rigorous viewpoint....

4. Height Fluctuations in Interacting Dimers

Prof. Alessandro Giuliani (Univ. Roma Tre)

10/06/2015, 12:00

Perfect matchings of Z^2 (also known as non-interacting dimers on the square lattice) are an exactly solvable 2D statistical mechanics model. It is known that the associated height function behaves at large distances like a massless gaussian field, with the variance of height gradients growing logarithmically with the distance. As soon as dimers mutually interact, via e.g. a local energy...

16. Singular Stochastic PDEs and Dynamical Field Theory Models

Pronob K. Mitter (Montpellier Univ. (France))

10/06/2015, 14:30

There is considerable interest at present in Singular Stochastic PDEs especially in connection with Rough Path Theory in different guises. The mathematical work started with results by Gianni Jona-Lasinio and myself a long time ago. I will review what was was accomplished at the time and the progress that has been made since then. One reason for presenting this to this audience is...

14. Large deviations for singular stochastic partial differential equations

Gianni Jona-Lasinio (INFN - Roma 1)

10/06/2015, 15:30

We consider SPDE's whose solutions are distribution-valued fields. An example is provided by the stochastic quantization of a scalar field in d=2,3 where infinite counter-terms are necessary. We review large deviation estimates for probabilistic weak solutions in d=2, derived long ago with P. K. Mitter, which show that the rate functional does not depend on the renormalization counter...

19. Probabilistic method in combinatorics using cluster expansion

Benedetto Scoppola (Univ. Tor Vergata Roma)

10/06/2015, 16:30

We will discuss the connection between the cluster expansion and the probabilistic method, used in order to give a-priori bounds for discrete combinatorics problems. Accurate estimates of the radius of convergence of the cluster expansion, as the Fernandez-Procacci construction, allow better estimates in the related combinatorics problems. We provide concrete examples of applications of...

8. Anomaly cancellation to all orders in chiral abelian gauge theories - A peturbative analysis based on (Bi)flow equations -

Christoph Kopper (Ecole Polytechnique Palaiseau)

11/06/2015, 09:30

We prove that the cancellation of the chiral anomaly in four-dimensional axial QED, as a consequence of a sum rule on the fermion charges, is valid to all orders in perturbation theory. The proof is based on analysing separately the fermionic and bosonic renormalization group flows.

20. Proof of a 43-year-old prediction by Wilson on anomalous scaling for a hierarchical composite field

Abdelmalek Abdesselam (Virginia Univ. (USA))

11/06/2015, 11:00

Hierarchical models a.k.a. the approximate recursion played a fundamental role in the discovery of the epsilon-expansion for critical exponents by Wilson and Fisher. In a not so well known 1972 article, Wilson showed, at the heuristic level, that at a nontrivial hierarchical model fixed point, the elementary field has no anomalous scaling whereas the composite square field does...

10. Renormalization Group Approach for the Optimally Doped Cuprates

Alvaro Ferraz (Rio Grande do Norte Univ. (Brazil))

11/06/2015, 12:00

We present an overview of the field-theoretical renormalzation group approach for interacting electrons in the normal phase of the optimally doped cuprates. Earlier calculations predicted the existence of d-wave charge density instabilities(d-CDW) which were later verifed in several experiments in non-Lanthanum materials. However the onset of the so-called pseudogap state remains an open...

1. Validity of Spin Wave Approximation for the Quantum Heisenberg Ferromagnet

Dr Michele Correggi (Roma Tre University)

11/06/2015, 14:30

We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins $ S \geq \frac{1}{2} $. We report on a rigorous proof of the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. Our proof comes with explicit, constructive upper and lower bounds on the error...

9. Quantum Phase Transition in an Interacting Fermionic Chain

Federico Bonetto (Georgia Tech - Atlanta)

11/06/2015, 15:30

We rigorously analyze the quantum phase transition between a metallic and an insulating phase in (non solvable) interacting spin chains or one dimensional fermionic systems. In particular, we prove the persistence of Luttinger liquid behavior in the presence of an interaction even arbitrarily close to the critical point, where the Fermi velocity vanishes and the two Fermi points...