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Tricritical phenomena in the Blume-Capel model.

Mathematics Colloquium | Trishen Gunaratnam | Feb 13th, 2024

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The Blume-Capel model is a ferromagnetic spin model that was introduced in the '60s to model an exotic phase transition in uranium oxide. Mathematically speaking, it is an Ising model coupled to a site percolation, combining two of the most beautiful models in statistical physics. It has a line of critical points – the Curie temperatures whereby the magnetisation-demagnetisation transition occurs. Along this critical line, the model is expected to undergo a further phase transition at the so-called tricritical point. Despite many fascinating physics conjectures concerning the tricritical universality class, there are few rigorous results. In this talk, I will discuss these conjectures and touch upon recent results joint with Dmitry Krachun (Princeton University) and Christoforos Panagiotis (University of Bath) in establishing the existence of a tricritical phenomenon in all dimensions.

About the Speaker: 

He is a mathematician working in probability theory. He is interested in the critical phenomena of percolation and spin models. 

He has been a postdoc at the Université de Genève advised by Hugo Duminil-Copin and Antti Knowles since Fall 2020.

From 2018-2020 he did his PhD in stochastic partial differential equations, where he was part of the group at Imperial College London. His advisers were Hendrik Weber (then University of Bath, now at the University of Munster) and Ajay Chandra (Imperial College London).


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