Symmetries and Probabilities in Lattice Models

Abstract: In statistical physics, one considers random models of large systems, whose individual components cannot be studied separately since there are so many of them (e.g., in 1g of iron there are approximately 10^22 iron molecules). Thus, properties of the system are described in terms of probability theory. Many interesting models, such as the so-called Ising model (describing magnetic material), enjoy symmetries that are useful when studying features of the model. In particular, so-called critical lattice models are symmetric with respect to conformal (injective, holomorphic) transformations in a certain sense. In this talk, we discuss how to make such a concept mathematically precise and how to understand probabilities of crossing events in such critical models. These questions have led to interesting discoveries in the mathematics community, such as the celebrated Schramm-Loewner evolution random curves and concepts trying to make sense of quantum field theory rigorously.

probability

Audience: researchers in the topic

Les probabilités de demain webinar

Series comments: There will be no seminar on 1st June because it is a public holiday in France (Pentecôte). The session on 15th June is the last one.