- Lecturer
- Vincent Tassion
- Coordinator
- Barbara Dembin

In this course we will provide a general introduction to the Ising model on finite graphs and on the hypercubic lattice \(\mathbf Z^d\) (main properties, standard mathematical tools).

Outline of the course:

- Definition of Ising model on a finite graph
- Random current representation and the switching lemma
- Correlation inequalities
- Phase transition
- Sharpness of the phase transition
- Stochastic domination and FKG inequality
- Infinite volume measures
- Uniqueness of the infinite volume measure

The lecture takes place in room HG D 1.2 and is given on the blackboard. The live stream (slides + sound, but no blackboard) can be accessed here .

Two exercise classes are scheduled for October 27, December 15 (replacing the regular lecture).

Office hours will take place in HG E65-2, each Monday, from 4pm to 6pm.

The lecture notes for the first part of the class are available below.

From November 3, the manuscript lecture notes can be found below

Every week, a new exercise sheet is uploaded here. Exercises that are marked with a star (*) can be handed in for correction (usually one per sheet). You can send them by email to barbara.dembin@math.ethz.ch or hand in before the lecture.

- Exercise sheet 1
- Exercise sheet 2
- Exercise sheet 3
- Exercise sheet 4
- Exercise sheet 5
- Exercise sheet 6
- Exercise sheet 7
- Exercise sheet 8
- Exercise sheet 9
- Exercise sheet 10
- Exercise sheet 11

- Lectures on the Ising and Potts models on the hypercubic lattice Lecture notes, Hugo Duminil-Copin.
- 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.