Pirogov-Sinai Theory and Singularity of the Ising Model on 𝕫² (2005)


These notes contain the technical part of the minicourse entitled "Introduction to Pirogov-Sinai Theory" I gave at the Universidade Federal de Minas Gerais, in april 2005. They contain a detailed analysis of the phase transition of the two-dimensional Ising model with a magnetic field, illustrating the most important ideas of Pirogov-Sinai Theory, although in a symmetric case.
Originally, the text was supposed to contain also a section on the study of the absence of analytic continuation following the technique of Isakov, but this was never written.
None of the material contained in these notes is original.

Keywords: Ising model, phase transition, phase diagram, Pirogov-Sinai Theory, cluster expansion.

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