Lecturer

Vincent Tassion

Coordinators

Abstract

In this course we will provide a general introduction to the Ising model on the hypercubic lattice \(\mathbf Z^d\) (main properties, standard mathematical tools). In order to answer important questions regarding the Ising model, we will exploit a deep connection of the model with a percolation processes, the Fortuin-Kastelen percolation.

Prerequisites

• Probability Theory.
• The course "Recent Development in Percolation Theory" (Autumn 2017) of Pierre Nolin is advised but not necessary (the overlap with Nolin's course will be minimal)

Lecture Notes

• Part 1: Ising Model - preliminary version (manuscript notes)
• Part 2: FK percolation - preliminary version (manuscript notes)

• Le modèle d'Ising. Lecture notes (in French), Ivan Velenik.
• Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction Book, Sacha Friedli and Yvan Velenik.
• Lectures on the Ising and Potts models on the hypercubic lattice Lecture notes, Hugo Duminil-Copin.