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CriBLaM SIGNED

Critical behavior of lattice models

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EC-Contrib. €

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Project "CriBLaM" data sheet

The following table provides information about the project.

Coordinator
INSTITUT DES HAUTES ETUDES SCIENTIFIQUES 

Organization address
address: ROUTE DE CHARTRES 35
city: BURES SUR YVETTE
postcode: 91440
website: www.ihes.fr

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 France [FR]
 Total cost 1˙499˙912 €
 EC max contribution 1˙499˙912 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-STG
 Funding Scheme ERC-STG
 Starting year 2018
 Duration (year-month-day) from 2018-09-01   to  2023-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    INSTITUT DES HAUTES ETUDES SCIENTIFIQUES FR (BURES SUR YVETTE) coordinator 1˙499˙912.00

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 Project objective

Statistical physics is a theory allowing the derivation of the statistical behavior of macroscopic systems from the description of the interactions of their microscopic constituents. For more than a century, lattice models (i.e. random systems defined on lattices) have been introduced as discrete models describing the phase transition for a large variety of phenomena, ranging from ferroelectrics to lattice gas.

In the last decades, our understanding of percolation and the Ising model, two classical exam- ples of lattice models, progressed greatly. Nonetheless, major questions remain open on these two models.

The goal of this project is to break new grounds in the understanding of phase transition in statistical physics by using and aggregating in a pioneering way multiple techniques from proba- bility, combinatorics, analysis and integrable systems. In this project, we will focus on three main goals:

Objective A Provide a solid mathematical framework for the study of universality for Bernoulli percolation and the Ising model in two dimensions. Objective B Advance in the understanding of the critical behavior of Bernoulli percolation and the Ising model in dimensions larger or equal to 3. Objective C Greatly improve the understanding of planar lattice models obtained by general- izations of percolation and the Ising model, through the design of an innovative mathematical theory of phase transition dedicated to graphical representations of classical lattice models, such as Fortuin-Kasteleyn percolation, Ashkin-Teller models and Loop models.

Most of the questions that we propose to tackle are notoriously difficult open problems. We believe that breakthroughs in these fundamental questions would reshape significantly our math- ematical understanding of phase transition.

 Publications

year authors and title journal last update
List of publications.
2020 M. Aizenman, H. Duminil-Copin, and S. Warzel
Dimerization and Néel order in different quantum spin chains through a shared loop representation
published pages: , ISSN: , DOI:
2020-04-24
2019 M. Aizenman, H. Duminil-Copin, V. Tassion and S. Warzel
Emergent Planarity in two-dimensional Ising Models with finite-range Interactions
published pages: 661-743, ISSN: 0020-9910, DOI:
Inventiones Mathematicae 216(3) 2020-04-24
2019 H. Duminil-Copin and M. Lis
On the double random current nesting field
published pages: 937-955, ISSN: 0178-8051, DOI:
Probability Theory and Related Fields 175(3-4) 2020-04-24
2020 H. Duminil-Copin, G. Kozma and V. Tassion
Upper bounds on the percolation correlation length
published pages: , ISSN: , DOI:
special volume in memory of Vladas Sidoravicius 2020-04-24
2020 Karrila, Alex
UST branches, martingales, and multiple SLE(2)
published pages: , ISSN: , DOI:
2020-04-24
2020 H. Duminil-Copin, S. Ganguly, A. Hammond and I. Manolescu
Bounding the number of self-avoiding walks: Hammersley-Welsh with polygon insertion
published pages: , ISSN: 0091-1798, DOI:
Annals of Probability 2020-04-24
2019 H. Duminil-Copin, A. Raoufi and V. Tassion
Exponential decay of connection probabilities for subcritical Voronoi percolation in $mathbb R^d$
published pages: 479–490, ISSN: 0178-8051, DOI:
Probability Theory and Related Fields 173(1–2) 2020-04-24
2020 M. Aizenman and H. Duminil-Copin
Marginal triviality of the scaling limits of critical 4D Ising and Ï•^4_4 models
published pages: , ISSN: , DOI:
2020-04-24
2020 H. Duminil-Copin, S. Goswami and A. Raoufi
Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature
published pages: 891–921, ISSN: 0010-3616, DOI:
Communications in Mathematical Physics 374(2) 2020-04-24
2020 H. Duminil-Copin, A. Glazman, R. Peled and Y. Spinka
Macroscopic loops in the loop O(n) model at Nienhuis’ critical point
published pages: , ISSN: 1435-9855, DOI:
Journal of European MAthematical Society 2020-04-24
2019 H. Duminil-Copin and V. Tassion
Renormalization of crossing probabilities in the planar random-cluster model
published pages: , ISSN: , DOI:
2020-04-24
2020 H. Duminil-Copin, S. Goswami, Rodriguez, Pierre-François and F. Severo
Equality of critical parameters for percolation of Gaussian free field level-sets
published pages: , ISSN: , DOI:
2020-04-24
2018 Drewitz, Alexander; Prévost, Alexis; Rodriguez, Pierre-François
Geometry of Gaussian free field sign clusters and random interlacements
published pages: , ISSN: , DOI:
2020-04-24
2019 H. Duminil-Copin, M. Harel, B. Laslier, A. Raoufi, G. Ray
Logarithmic variance for the height function of square-ice
published pages: , ISSN: , DOI:
2020-04-24
2019 H. Duminil-Copin, S. Goswami, A. Raoufi, F. Severo and A. Yadin
Existence of phase transition for percolation using the Gaussian Free Field
published pages: , ISSN: 0012-7094, DOI:
Duke Mathematical Journal 2020-04-24
2020 H. Duminil-Copin, A. Raoufi and V. Tassion
Subcritical phase of d-dimensional Poisson-Boolean percolation and its vacant set
published pages: , ISSN: , DOI:
Annales Henry Lebesgue 2020-04-24
2019 H. Duminil-Copin, A. Raoufi and V. Tassion
Sharp phase transition for the random-cluster and Potts models via decision trees
published pages: Princeton Univer, ISSN: 0003-486X, DOI:
Annals of Mathematics 189(1) 2020-04-24

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