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Universality in Condensed Matter and Statistical Mechanics

Total Cost €


EC-Contrib. €






Project "UniCoSM" data sheet

The following table provides information about the project.


Organization address
address: VIA OSTIENSE 159
city: ROMA
postcode: 154

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Italy [IT]
 Total cost 1˙235˙875 €
 EC max contribution 1˙235˙875 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-COG
 Funding Scheme ERC-COG
 Starting year 2017
 Duration (year-month-day) from 2017-03-01   to  2022-02-28


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITA DEGLI STUDI ROMA TRE IT (ROMA) coordinator 1˙235˙875.00


 Project objective

Universality is a central concept in several branches of mathematics and physics. In the broad context of statistical mechanics and condensed matter, it refers to the independence of certain key observables from the microscopic details of the system. Remarkable examples of this phenomenon are: the universality of the scaling theory at a second order phase transition, at a quantum critical point, or in a phase with broken continuous symmetry; the quantization of the conductivity in interacting or disordered quantum many-body systems; the equivalence between bulk and edge transport coefficients. Notwithstanding the striking evidence for the validity of the universality hypothesis in these and many other settings, a fundamental understanding of these phenomena is still lacking, particularly in the case of interacting systems.

This project will investigate several key problems, representative of different instances of universality. It will develop along three inter-connected research lines: scaling limits in Ising and dimer models, quantum transport in interacting Fermi systems, continuous symmetry breaking in spin systems and in models for pattern formation or nematic order. Progresses on these problems will come from an effective combination of the complementary techniques that are currently used in the mathematical theory of universality, such as: constructive renormalization group, reflection positivity, functional inequalities, discrete harmonic analysis, rigidity estimates. We will pay particular attention to the study of some poorly understood aspects of the theory, such as the role of boundary corrections, the loss of translational invariance in multiscale analysis, and the phenomenon of continuous non-abelian symmetry breaking. The final goal of the project is the development of new tools for the mathematical analysis of strongly interacting systems. Its impact will be an improved fundamental understanding of universality phenomena in condensed matter.


year authors and title journal last update
List of publications.
2019 Domenico Monaco, Stefan Teufel
Adiabatic currents for interacting fermions on a lattice
published pages: 1950009, ISSN: 0129-055X, DOI: 10.1142/s0129055x19500090
Reviews in Mathematical Physics 31/03 2019-11-07
2019 Horia D. Cornean, Domenico Monaco, Massimo Moscolari
Parseval Frames of Exponentially Localized Magnetic Wannier Functions
published pages: , ISSN: 0010-3616, DOI: 10.1007/s00220-019-03542-0
Communications in Mathematical Physics 2019-11-07
2019 Giuliani, Alessandro; Mastropietro, Vieri; Porta, Marcello
Quantization of the interacting Hall conductivity in the critical regime
published pages: , ISSN: , DOI:
Journal of Statistical Physics (to appear) 2019-11-07
2019 Disertori, Margherita; Giuliani, Alessandro; Jauslin, Ian
Plate-nematic phase in three dimensions
published pages: , ISSN: , DOI:
Communications in Mathematical Physics (to appear) 2019-11-07
2019 Erignoux, Clément; Simon, Marielle
Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise
published pages: , ISSN: , DOI: 2019-11-07
2019 Alessandro Giuliani, Vieri Mastropietro, Fabio Toninelli
Non-integrable dimers: Universal fluctuations of tilted height profiles
published pages: , ISSN: , DOI: 2019-11-07
2019 Horia D. Cornean, David Gontier, Antoine Levitt, Domenico Monaco
Localised Wannier Functions in Metallic Systems
published pages: 1367-1391, ISSN: 1424-0637, DOI: 10.1007/s00023-019-00767-6
Annales Henri Poincaré 20/4 2019-11-07
2019 Alessandro Giuliani, Fabio Lucio Toninelli
Non-integrable dimer models: Universality and scaling relations
published pages: 103301, ISSN: 0022-2488, DOI: 10.1063/1.5109618
Journal of Mathematical Physics 60/10 2019-11-07
2019 Francis Comets, Giambattista Giacomin, Rafael L. Greenblatt
Continuum Limit of Random Matrix Products in Statistical Mechanics of Disordered Systems
published pages: 171-219, ISSN: 0010-3616, DOI: 10.1007/s00220-019-03466-9
Communications in Mathematical Physics 369/1 2019-11-07
2019 Giuliani, A.; Mastropietro, V.; Porta, M.
Anomaly non-renormalization in interacting Weyl semimetals
published pages: , ISSN: , DOI: 2019-11-07
2019 Giuliani, Alessandro; Theil, Florian
Long range order in atomistic models for solids
published pages: , ISSN: , DOI: 2019-11-07
2017 Giuliani, Alessandro
Order, disorder and phase transitions in quantum many body systems
published pages: , ISSN: , DOI: 2019-11-07
2018 Giovanni Antinucci, Vieri Mastropietro, Marcello Porta
Universal Edge Transport in Interacting Hall Systems
published pages: 295-359, ISSN: 0010-3616, DOI: 10.1007/s00220-018-3192-y
Communications in Mathematical Physics 362/1 2019-07-18
2017 Vieri Mastropietro, Marcello Porta
Spin Hall insulators beyond the helical Luttinger model
published pages: , ISSN: 2469-9950, DOI: 10.1103/PhysRevB.96.245135
Physical Review B 96/24 2019-07-18
2018 Vieri Mastropietro, Marcello Porta
Canonical Drude Weight for Non-integrable Quantum Spin Chains
published pages: 379-397, ISSN: 0022-4715, DOI: 10.1007/s10955-018-1994-0
Journal of Statistical Physics 172/2 2019-07-18

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