Lectures in course MATH-486: Statistical mechanics and Gibbs measures

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

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

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

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

Explores the Lee-Yang theory, covering connected graphs, paths, phase diagrams, and analytic continuation.

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

Introduces Gibbs measures to describe systems on an infinite lattice.

Covers the definition of Gibbs measures, proper kernels, compatibility, phase transitions, and existence conditions.