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CONSTAMIS SIGNED

Connecting Statistical Mechanics and Conformal Field Theory: an Ising Model Perspective

Total Cost €

EC-Contrib. €

Partnership

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CONSTAMIS project word cloud

Explore the words cloud of the CONSTAMIS project. It provides you a very rough idea of what is the project "CONSTAMIS" about.

structures connection started blocks reveal integrable chapter appear convergence parafermions arising proven minimal dimensions symmetry mathematical mechanics theories physics rigorous cft correspondence gather applicable ising algebras quantum converge conjectural physical unfortunately subjects gap achievements close theorems symmetric extremely reveals light connections bridges theory link massive remarkable enabled ed powerful picture potentially spectacular derivations frameworks first formulae theoretic models objects investigations half conformal links science ago remained statistical mathematics breakthroughs clear 20th insights scientists shed connect combine model linking made sle leaving deep progress conformally theoretical precise century 15 discrete curves predicted connecting building

Project "CONSTAMIS" data sheet

The following table provides information about the project.

Coordinator	ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE Organization address address: BATIMENT CE 3316 STATION 1 city: LAUSANNE postcode: 1015 website: www.epfl.ch 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	Switzerland [CH]
Total cost	998˙005 €
EC max contribution	998˙005 € (100%)
Programme	1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
Code Call	ERC-2016-STG
Funding Scheme	ERC-STG
Starting year	2017
Duration (year-month-day)	from 2017-03-01 to 2022-02-28

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE Organization address address: BATIMENT CE 3316 STATION 1 city: LAUSANNE postcode: 1015 website: www.epfl.ch contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	CH (LAUSANNE)	coordinator	998˙005.00

Map

Project objective

The developments of Statistical Mechanics and Quantum Field Theory are among the major achievements of the 20th century's science. During the second half of the century, these two subjects started to converge. In two dimensions, this resulted in a most remarkable chapter of mathematical physics: Conformal Field Theory (CFT) reveals deep structures allowing for extremely precise investigations, making such theories powerful building blocks of many subjects of mathematics and physics. Unfortunately, this convergence has remained non-rigorous, leaving most of the spectacular field-theoretic applications to Statistical Mechanics conjectural.

About 15 years ago, several mathematical breakthroughs shed new light on this picture. The development of SLE curves and discrete complex analysis has enabled one to connect various statistical mechanics models with conformally symmetric processes. Recently, major progress was made on a key statistical mechanics model, the Ising model: the connection with SLE was established, and many formulae predicted by CFT were proven.

Important advances towards connecting Statistical Mechanics and CFT now appear possible. This is the goal of this proposal, which is organized in three objectives:

(I) Build a deep correspondence between the Ising model and CFT: reveal clear links between the objects and structures arising in the Ising and CFT frameworks.

(II) Gather the insights of (I) to study new connections to CFT, particularly for minimal models, current algebras and parafermions.

(III) Combine (I) and (II) to go beyond conformal symmetry: link the Ising model with massive integrable field theories.

The aim is to build one of the first rigorous bridges between Statistical Mechanics and CFT. It will help to close the gap between physical derivations and mathematical theorems. By linking the deep structures of CFT to concrete models that are applicable in many subjects, it will be potentially useful to theoretical and applied scientists.

Publications

List of publications.
year	authors and title	journal	last update
2019	Sung Chul Park, ClÃ©ment Hongler Ising Model and Field Theory: Lattice Local Fields and Massive Scaling Limit published pages: , ISSN: , DOI: 10.5075/epfl-thesis-7741		2019-09-26
2019	Reza Gheissari, ClÃ©ment Hongler, S. C. Park Ising Model: Local Spin Correlations and Conformal Invariance published pages: 771-833, ISSN: 0010-3616, DOI: 10.1007/s00220-019-03312-y	Communications in Mathematical Physics 367/3	2019-09-26
2019	StÃ©phane Benoist, ClÃ©ment Hongler The scaling limit of critical Ising interfaces is $mathrm{CLE}_{3}$ published pages: 2049-2086, ISSN: 0091-1798, DOI: 10.1214/18-aop1301	The Annals of Probability 47/4	2019-09-17

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