A geometric approach to the Ising model


Hugo Duminil-Copin

University of Geneva

Northeastern University

Thursday, November 19, 2015


Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 553 Lake Hall


Abstract: The Ising model is a model for the loss of magnetization of real-life magnets above a critical temperature called Curie's temperature (named after Pierre Curie who discovered the phenomenon in his thesis). Since its introduction in the beginning of the 20th century, it became one of the most studied model of statistical physics.

Even though the model is easy to define, it is a beautiful field of study involving divers domains of mathematics, for instance combinatorics, algebra, complex analysis, field theory and probabilities. Many aspects of the behavior of the model are now understood, but many other aspects are still resisting attacks by physicists and mathematicians.

In this talk, we will define the Ising model and present some of its basic properties. We will also describe a geometric approach based on the notion of random current, introduced by Michael Aizenman in 1980 and explain how this approach can be used to understand the critical behavior of the model. In particular, we will mention a recent results regarding the transition in three dimensions.

Here are some directions to Northeastern University. Lake Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from one of NEU colloquium organizers.

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Posted: November 10, 2015    URL: