Objective
Statistical mechanics is concerned with the emergent macroscopic behaviour of systems consisting of interacting microscopic particles. Lattice models form a subclass of such systems where the particles are placed on a lattice (grid), and provide a mathematical framework for studying this emergent behaviour. We are particularly interested in phase transitions, where a small change in the parameters of the model leads to a radical change in the macroscopic behaviour of the system.
In lattice models, the key quantities (e.g. correlation functions) are often encoded in terms of random geometrical objects. In the special case of models with a percolation representation (e.g. Bernoulli percolation, the Ising model), spectacular progress has been made in the past decades. In a large number of natural models, however, the relevant geometrical objects are not clusters (connected components of random subgraphs of the lattice), but rather random families of loops and paths on the lattice (e.g. the XY model, the Heisenberg model, height functions).
Recent insights suggest that striking progress on loop-based models can be made in the next few years. The objective of this project is to break new ground on the fundamental understanding of phase transitions via structural changes in the random loops. This will require significant innovations, combining techniques from probability, combinatorics, analysis, and mathematical physics. Our ambition is to make breakthrough progress on open problems in three central areas:
* The Berezinskii--Kosterlitz--Thouless transition (which led to the 2016 physics Nobel Prize);
* Phase transitions in the XY model in dimension three and higher;
* The Polyakov conjecture for the two-dimensional Heisenberg model.
Even limited progress would clarify the mathematics of critical phenomena of lattice models, which serve as pillars for modern theoretical physics.
Fields of science (EuroSciVoc)
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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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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
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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.
HORIZON-ERC - HORIZON ERC Grants
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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-2026-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.
75794 Paris
France
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.