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.
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
ERC-STG - Starting Grant
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2017-STG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
91440 Bures Sur Yvette
France
The organization defined itself as SME (small and medium-sized enterprise) at the time the Grant Agreement was signed.
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.