Course

MATH-486: Statistical mechanics and Gibbs measures

Summary

This course provides a rigorous introduction to the ideas, methods and results of classical statistical mechanics, with an emphasis on presenting the central tools for the probabilistic description of infinite lattice systems.

Lectures

Instructor

Sacha Friedli

Diploma of Physics, Université de Lausanne, 1999 Phd, Institut de Physique Théorique, EPFL, 1999-2004 Post-doc, IMPA (Instituto Nacional de Matemática Pura e Aplicada), Rio de Janeiro, Brasil, 2004-2006 Adjunct professor, Departamento de Matemática (Universidade Federal de Minas Gerais), 2006-2016 Collaborateur Scientifique, Cours de Mathématiques Spéciales, EPFL, Lausanne, 2016-

Official source

https://edu.epfl.ch/coursebook/en/statistical-mechanics-and-gibbs-measures-MATH-486

Moodle Page

http://go.epfl.ch/MATH-486

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Summary

Lectures

Instructor

Sacha Friedli

Official source

https://edu.epfl.ch/coursebook/en/statistical-mechanics-and-gibbs-measures-MATH-486

Moodle Page

http://go.epfl.ch/MATH-486

About this result

Lectures in this course (8)

Existence of Gibbs measures

Explores quasilocality in statistical mechanics and the existence conditions of Gibbs measures.

The inhomogeneous Ising chain

Covers the inhomogeneous Ising chain, Gibbs measures, and the Borel-Cantelli lemma.

Extremal Gibbs measures, Uniqueness

Explores extremal Gibbs measures and uniqueness in statistical mechanics, covering properties and conditions for uniqueness.

Phase diagram of the Ising model

Explores the phase diagram of the Ising model, focusing on Gibbs state uniqueness and critical temperatures.

Peierls argument

Explores the Peierls argument and its application in the Ising Model.

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