The goal of this project is to write an introductory book on statistical mechanics. As there are already many such books, both for physicists and mathematicians, we believe it is important to describe what we aim to achieve. We decided to write a book that is
  • of limited scope: although we plan to cover many important topics, we have decided to limit the scope of our book. Among the most important topics that we won't be discussing (except possibly in short notes), let us list: quantum models, non-lattice models, disordered systems, critical phenomena (critical exponents, critical scaling limits, etc.), stochastic dynamics.
  • student-friendly: we plan to make the book as readable as possible, accessible to advanced undergraduates (say, master level), both in mathematics and physics. To achieve this end, we shall refrain from stating and proving the most general claims possible, but shall instead discuss in detail particularly important examples. We also want the book to be more or less self-contained, which means, in particular, that there will be appendices introducing the required mathematical tools. Also, solutions to most exercises will be given.
  • based on the probabilistic approach to (rigorous) equilibrium statistical mechanics, even though we won't refrain from using other types of tools when needed. In particular, there won't be much discussion of explicit solutions for integrable models.
Below, you can find the draft of the book, as it was sent to the publisher, Cambridge University Press, on August 26, 2016. Typos, corrections, suggestions can be sent to us at introsmbook@gmail.com. We will implement the needed corrections on the version on this page as they are found (check the date associated to the files below to see which ones have been updated, or have a look at the errata).

Dobrushin's rigid interface between two equilibrium phases in the low-temperature 3d Ising lattice gas

Note [May 11, 2015]: Claudio Landim (IMPA) has recently given a course based on Chapter 3 (The Ising model). Videos of the lectures can be found here (see lectures 1 to 9); the lectures are in Portuguese.

Note [January 19, 2016]: One of us (Y.V.) has recently given a one-semester course, entitled Introduction to Statistical Mechanics, based on Chapters 3, 7, 8 and 10. Videos of the lectures (as well as other lectures in the same program) have been uploaded here.

Note [March 22, 2016]: As you may have noted, the title of the book has been shortened, after discussion with the book's future publisher. This is the final title.

Files

Complete book (version: September 2 2016) [ERRATA]

Title and table of contents (version: August 25 2016)

  1. Foreword (to be written)
  2. Introduction (version: August 25 2016)
  3. The Curie-Weiss Model (version: September 2 2016)
  4. The Ising Model (version: August 25 2016)
  5. Liquid-Vapor Equilibrium (version: August 25 2016)
  6. Cluster Expansion (version: August 25 2016)
  7. Infinite Volume Gibbs Measures (version: August 25 2016)
  8. Pirogov-Sinai Theory (version: August 25 2016)
  9. The Gaussian Free Field on Z^d (version: August 25 2016)
  10. Models With Continuous Symmetry (version: August 25 2016)
  11. Reflection Positivity (version: August 25 2016)
  12. Notes (version: August 25 2016)
  13. Mathematical Appendices (version: August 25 2016)
  14. Solutions To The Exercises (version: August 25 2016)
  15. Bibliography (version: August 25 2016)
  16. Index (version: August 25 2016)