Project description
Advancing the mathematical theory of critical phenomena
The mathematical theory of critical phenomena has garnered significant interest due to its relevance across various fields. Despite recent advancements, second-order phase transitions in three or more dimensions remain elusive, posing a major challenge for researchers. The ERC-funded UniCorn project aims to advance this theory by investigating related models and theories that exhibit long-range correlations. By addressing key open questions, the project will develop a near-critical scaling theory for continuous phase transitions in these models, contributing to the broader understanding of critical phenomena and their applications.
Objective
The objective of this project is to develop the mathematical theory of critical phenomena. In spite of recent breakthroughs, second-order phase transitions have remained largely elusive in dimensions 3 and higher and represent a formidable challenge. The project will make headway on this and related fundamental problems, especially in the hard intermediate dimensions.
The expected outcomes of this proposal will provide prime rigorous results that determine the scaling behaviour of certain non-planar percolation models near their critical point. Its findings are meant to put a heuristic scaling theory originating from physics on firm mathematical foundations. This theory is at the heart of modern computational methods and goes back to foundational (Nobel-prize winning) work on renormalisation.
Universality is the guiding principle by which the behaviour of many physical systems ought to be largely independent of the specifics of the model considered and instead only depend on a few key parameters. The project is designed as a full-fledged study of several judiciously chosen models with long-range (LR) correlations, which my recent works have identified as ideal candidates for a rigorous investigation. These benefit from a rich mathematical structure stemming from the interplay between percolation and random walks, which can be forcefully exploited.
Building on my recent results, I plan to tackle a series of questions, in order to:
(1) identify and describe their off-critical phases;
(2) prove the existence of critical exponents exhibiting (hyper-)scaling;
(3) investigate scaling limits of critical clusters and study their fractal geometry.
The outcomes of steps (1)-(3) will give rise to a rigorous (near-)critical scaling theory for the continuous phase transition associated to these LR-models, and identify their universality classes. In so doing the project will also tackle several related problems in disordered systems and random media.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
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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)
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.
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-2024-COG
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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.
CB2 1TN CAMBRIDGE
United Kingdom
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.