Lectures on Phase Transitions and the Renormalization Group

Frontiers in Physics

by Nigel Goldenfeld

Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.

Genres: Physics, Science, Textbooks

420 pages, Paperback

First published January 1, 1992

Reviews

[Johannes · Rating 5 out of 5]

Universality is the idea that a large number of different physical systems in the same "class" will share common behavior, eg scaling laws. This is possible when the behavior depends exclusively on certain characteristics and not on the details of the individual systems (course graining). Although this idea was not a new one, the computation of critical exponents in thermodynamic systems remained imprecise for many years because it was not well understood what the relevant characteristics were. Only with the introduction of the renormalization was this mystery fully solved.

This text starts at the beginning: Ising model, mean field theories, etc. From there, it builds up through improved theories (eg Landau) and introduces important concepts like symmetry and ergodicity breaking as needed along the way. Finally we reach RG, and the student will be amazed at how (relatively) simple the correct description is! Yet, despite its simplicity, it is easy to understand why RG took so long in coming. The concept is truly brilliant.

This book is wonderfully written. The notation and typesetting are a bit uninspiring, but by the time one is ready for a work of this level, one should be able to adapt to these minor difficulties.

A reasonably good background in stat mech is necessary, and for RG in particular some knowledge of nonlinear dynamics is recommended.

[Lucas · Rating 5 out of 5]

There was an exercise so hard I almost learned russian to read the paper Goldenfeld based it on

[Michael · Rating 5 out of 5]

I found this book to be the most readable explanation of RG theory. The extensively worked example cases and generous explanations distinguish this book from other similar books. Highly recommended.

[Filippo Elgorni · Rating 4 out of 5]

I didn’t understand everything in this book, a thing that makes me kinda sad about my intentions to keep studying of physics after graduation, but overall I am happy to have taken this little journey. For as many chapters I didn’t understand, there are as many that were easily enlightening, and I finally can tell that at least *some* of the pillars of this beautiful theory are now clear to me. Many other sections were anyways engaging, and provided some insight that I can keep for later :)

[Ryan McKenzie · Rating 5 out of 5]

This is a classic text on statistical physics and the theory of phase transitions. I read it cover to cover when I was learning the subject, and I continue to use it as a reference today. I'd highly recommend the book to anyone interested in the subject.

[Navid Aliakbarian · Rating 4 out of 5]

The author has worked very tastefully and carefully in writing this book.

[Sthitadhi Roy · Rating 3 out of 5]

a good book, at the introductory level, especially the balance between what should be worked out in the text and what should be left to the readers is very good. The exercises are quite nice, the reader is guided through them and they are not merely problems, they are actually explanations of new concepts. However, the book also has some flaws, the student would need a teacher to help him/her with the book, as quite often new notations and concepts are invoked without properly introducing them, also some things are done quite superficially which make sense only in that particular context and not in general, this can be quite confusing for the reader.
Overall, a good book and very very readable