The goal of this ongoing 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. Our plan is 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.
On this page, early drafts of chapters from our book will be made available (as soon as we think them presentable), and updated as frequently as possible. We would be very happy to receive corrections, suggestions, constructive criticisms from our readers, so don't hesitate to contact us at introsmbook@gmail.com.

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.

Files

Warning: The chapters below are early drafts. As such, they are likely to contain mistakes and be incomplete (in case you find any mistake, or if you believe that some important topics are missing, please tell us!). Also, bibliographical information may be only partial, or even completely inexistent, depending on the stage of writing. We apologize in advance to all the people whose works are not (yet!) properly referenced.

Table of contents (latest version: July 1 2015)

  1. Introduction (latest version: June 18 2015; in progress, still very incomplete)
  2. Mean field models (latest version: June 18 2015)
  3. The Ising model (latest version: July 1 2015)
  4. The liquid-vapor equilibrium (latest version: April 1 2015)
  5. The cluster expansion (latest version: July 1 2015)
  6. Infinite volume Gibbs measures (latest version: July 1 2015)
  7. The Gaussian Free Field (latest version: July 1 2015)
  8. Models with continuous symmetry (latest version: July 1 2015)
  9. Reflection positivity and applications
  10. Long-range Ising model
  11. Large deviations and the equivalence of ensembles
  12. Pirogov-Sinai theory
  13. Mathematical appendices (latest version: June 18 2015; in progress, still very incomplete)
  14. Solutions to the exercises
  15. Bibliography
  16. Index