Universality in Condensed Matter and Statistical Mechanics

Projektinformationen

UniCoSM

ID Finanzhilfevereinbarung: 724939

DOI 10.3030/724939

Abgeschlossenes Projekt

EK-Unterschriftsdatum 30 Januar 2017

Startdatum 1 März 2017

Enddatum 28 Februar 2023

Finanziert unter

• EXCELLENT SCIENCE - European Research Council (ERC)

Gesamtkosten € 1 235 875,00

EU-Beitrag € 1 235 875,00

Koordiniert durch

UNIVERSITA DEGLI STUDI ROMA TRE
Italy

Ziel

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.

Wissenschaftliches Gebiet

• natural sciences › mathematics › pure mathematics › mathematical analysis
• natural sciences › physical sciences › classical mechanics › statistical mechanics

Schlüsselbegriffe

• Scaling limits
• conformal invariance
• quantum transport
• continuous symmetry breaking
• spin models
• interacting Fermi systems
• renormalization group
• reflection positivity
• pattern formation

Programm/Programme

• H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme

Thema/Themen

• ERC-2016-COG - ERC Consolidator Grant

Aufforderung zur Vorschlagseinreichung

ERC-2016-COG

Finanzierungsplan

ERC-COG - Consolidator Grant

Gastgebende Einrichtung

UNIVERSITA DEGLI STUDI ROMA TRE

• Netto-EU-Beitrag: € 1 235 875,00
• Adresse: VIA OSTIENSE 133 ; 00154 Roma ; Italien
• Region: Centro (IT) › Lazio › Roma
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: € 1 235 875,00

Begünstigte (1)

UNIVERSITA DEGLI STUDI ROMA TRE

Italien

• Netto-EU-Beitrag: € 1 235 875,00
• Adresse: VIA OSTIENSE 133 ; 00154 Roma
• Region: Centro (IT) › Lazio › Roma
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: € 1 235 875,00