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. Fields of science natural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Keywords Statistical Physics Phase transition percolation theory Ising model Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2017-STG - ERC Starting Grant Call for proposal ERC-2017-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Host institution INSTITUT DES HAUTES ETUDES SCIENTIFIQUES Net EU contribution € 1 301 459,31 Address ROUTE DE CHARTRES 35 91440 Bures Sur Yvette France See on map SME The organization defined itself as SME (small and medium-sized enterprise) at the time the Grant Agreement was signed. Yes Region Ile-de-France Ile-de-France Essonne Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 301 459,31 Beneficiaries (2) Sort alphabetically Sort by Net EU contribution Expand all Collapse all INSTITUT DES HAUTES ETUDES SCIENTIFIQUES France Net EU contribution € 1 301 459,31 Address ROUTE DE CHARTRES 35 91440 Bures Sur Yvette See on map SME The organization defined itself as SME (small and medium-sized enterprise) at the time the Grant Agreement was signed. Yes Region Ile-de-France Ile-de-France Essonne Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 301 459,31 UNIVERSITE DE GENEVE Switzerland Net EU contribution € 198 452,69 Address RUE DU GENERAL DUFOUR 24 1211 Geneve See on map Region Schweiz/Suisse/Svizzera Région lémanique Genève Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 198 452,69
