Lecture

The inhomogeneous Ising chain

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In course

MATH-486: Statistical mechanics and Gibbs measures

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. ...

Description

This lecture introduces the inhomogeneous Ising chain, focusing on the definition of the kernel T and Gibbsian specifications. It covers the construction of Gibbs measures, the thermodynamic limit, and the properties of the Ising model. The lecture also discusses the computation of Gibbs measures and the simplifying features of the model, emphasizing the inhomogeneous Ising chain on a lattice. Various propositions and lemmas are presented to illustrate the concepts, including the change of variables and the extension of measures. The lecture concludes with the Borel-Cantelli lemma and the implications of events occurring simultaneously.

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