- 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.
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.
Note [February 20, 2017]: As you may have noted, the numbering of the theorems, exercises, etc, has been changed, so that each category has its own separate numbering. This was done at the request of the book's future publisher. We apologize for any inconvenience that this change might cause.
Note [April 25, 2017]: As you may have noted, the numbering of the theorems, exercises, etc, has been changed once more, so that all categories, except the exercises, share a common numbering. This was done at the request of the book's future publisher. We apologize for any inconvenience that this change might cause. THIS WILL NOT CHANGE ANYMORE.
Files
Complete book (version: April 25 2017) [ERRATA]
Front matter (version: April 25 2017)
- Chapter 1. Introduction (version: April 25 2017)
- Chapter 2. The Curie-Weiss Model (version: April 25 2017)
- Chapter 3. The Ising Model (version: April 25 2017)
- Chapter 4. Liquid-Vapor Equilibrium (version: April 25 2017)
- Chapter 5. Cluster Expansion (version: April 25 2017)
- Chapter 6. Infinite Volume Gibbs Measures (version: April 25 2017)
- Chapter 7. Pirogov-Sinai Theory (version: April 25 2017)
- Chapter 8. The Gaussian Free Field on Z^d (version: April 25 2017)
- Chapter 9. Models With Continuous Symmetry (version: April 25 2017)
- Chapter 10. Reflection Positivity (version: April 25 2017)
- Appendix A. Notes (version: April 25 2017)
- Appendix B. Mathematical Appendices (version: April 25 2017)
- Appendix C. Solutions To The Exercises (version: April 25 2017)
- Bibliography (version: April 25 2017)
- Index (version: April 25 2017)