Learning outcome To give the students a general background to thermodynamics and statistical physics. Admission Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb. Teaching The course is given in the spring term and contains up to 6 hours of teaching 4 h of lectures and 2 h of exercises per week. Examination Compulsory exercises.

Explanations and appeals Explanation of grades and appeals Resit an examination This course offers both postponed and resit of examination. Evaluation The course is subject to continuous evaluation.

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Facts about this course Credits 10 Level Master Teaching Every spring If the course is offered, a minimum of four students is required for ordinary lectures to take place. Examination Every spring Teaching language Norwegian English on request. Contact Department of Physics. Knutepunktet Speak up Registrations, deadlines and student card Special needs and leave of absence Leave of absence and reduced progress Start of studies. Examinations Submissions. Admission Why choose UiO?

Contact us Contact UiO. Scope Statistical mechanics and thermodynamics form an essential link between the properties of molecules and the behaviour of macroscopic matter. Get Involved We are always looking for new members who are keen to get involved and to help organise our activities.

## PHYS4031 Statistical Mechanics

If you would like to find out more please contact the Secretary. We then complement that with a discussion of correlations decay. Download Chapter 9 [version: July 22 ]. Reflection positivity is another tool that plays a central role in the rigorous study of phase transitions. We first expose it in detail, proving its two central estimates: the infrared bound and the chessboard estimate.

We then apply the latter to obtain several results of importance.

### Latest Research and Reviews

Combined with the results of Chapter 9, this provides a detailed description of this type of systems in the thermodynamic limit. Download Chapter 10 [version: July 22 ]. In this appendix, we introduce various mathematical topics used throughout the book, which might not be part of all undergraduate curricula.

For example: elementary properties of convex functions, some aspects of complex analysis, measure theory, conditional expectation, random walks, etc.

## b. What is statistical mechanics?

Download Appendix B [version: July 22 ]. Hints or detailed solutions for most of the exercises of the book can be found in this appendix. Download Appendix C [version: July 22 ]. Rigorous Statistical Mechanics has a long tradition, starting in the s with Dobrushin, Lanford, Ruelle, Sinai and many other mathematical physicists.

Yet, surprisingly, there has not been an up-to-date textbook on an introductory level.

This gap is bridged masterly by the present book. It addresses the curious newcomer by employing a carefully designed structure, which starts from a physics introduction and then uses the two-dimensional Ising model as a stepping-stone towards the richness of the subject.

### Course description

The book will be enjoyed by students and researchers with an interest in either theoretical condensed matter physics or probability theory. An excellent introduction to classical equilibrium statistical mechanics. There is clear concern with the understanding of ideas and concepts behind the various tools and models.

Topics are presented through examples, making this book a genuine 'concrete mathematical introduction'. While reading it, my first wish was to use it as soon as possible in a course. It is a 'must' for the libraries of graduate programs in mathematics or mathematical physics. This book is a marvelous introduction to equilibrium statistical mechanics for mathematically inclined readers, which does not sacrifice clarity in the pursuit of mathematical rigor. The book starts with basic definitions and a crash course in thermodynamics, and gets to sophisticated topics such as cluster expansions, the Pirogov-Sinai theory and infinite volume Gibbs measures through the discussion of concrete models.

This book should be on the bookshelf of any serious student, researcher and teacher of mathematical statistical mechanics. Ofer Zeitouni, Weizmann Institute, Israel. Sacha Friedli and Yvan Velenik have succeeded in writing a unique, modern treatise on equilibrium statistical mechanics.

They cover many fundamental concepts, techniques and examples in a didactic manner, providing a remarkable source of knowledge, grounded and refined by years of experience.

Stimulating and appealing, this book is likely to inspire generations of students and scientists. The authors have created an impressive book that shows its strengths in several ways: thoughtful organization and a well-designed presentation, real attention to the needs of the reader, and a very nice guide to the existing literature.

It could be a model of how mathematical physics should be presented. Our goal was to write a book that is of limited scope : although we cover many important topics, we decided to limit the scope of the book.

## PHYS4031 Statistical Mechanics

Among the most important topics that are not discussed except, occasionally, in short notes , let us list: quantum models, non-lattice models, disordered systems, critical phenomena, stochastic dynamics. To achieve this end, we have refrained from stating and proving the most general claims possible, but discussed instead in detail particularly important classes of examples among which the Ising model, the Curie-Weiss model, the Blume-Capel model, the Gaussian Free Field, the XY model, the Heisenberg model, etc. We also wanted the book to be more or less self-contained, so that we have included a rather long appendix introducing the required mathematical tools, and provided solutions to most of the exercises.

In particular, there is no discussion of explicit solutions for integrable models apart from brief comments. Reference to the published version Friedli, S. Files Here, you can find the final draft of the book. Download the complete book [version: July 22 , with some typos fixed September 20 ] Download the errata [version: September 20 ] Front matter Download Front Matter [version: July 22 ].

Chapter 1. Introduction In this chapter, we briefly and somewhat heuristically introduce equilibrium thermodynamics and equilibrium statistical mechanics, explaining the links between these two theories.