Lectures On Phase Transitions And The Renormalization Group (Frontiers in Physics Book 85) 1st Edition by Nigel Goldenfeld (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Nigel Goldenfeld: “…simply and clearly why phase transitions exist. ..” and “…to avoid technicalities which hide the crux of the matter…” These goals have been achieved. A student of this difficult subject will find here excellent discussions pertaining to: dimensional analysis ( “of the diffusion equation,” page 290), Ising model (“What may be simple to state may not be simple to solve,” page 9), lattice gas model (“statistical mechanics of a fluid,” page 74), correlation functions (“actually a Green function,” page 159), transfer matrices (“first introduced by Kramers,” page 85), mean field theory and functional integrals (” a sum over all smoothly varying functions,” page 153).The challenging exercises include hints, or steps, to prod the student to a solution (You will “derive” Wick’s Theorem, page 187). The physical discussions are lucid and pedagogic. Mathematical derivations are presented in a fashion which can hardly be made more explicit. The derivations can be followed with paper and pencil in hand (I trust that even in the age of computers certain routine computations and manipulations need to be actively assailed by the student). Particular mention goes to the fine discussion of similarity solutions and renormalisation in a general setting (chapter ten). We read: “the physical interpretation is quite straightforward. Renormalisation cures the problem of divergences, but still does not lead to anomalous dimensions.” (page 288). However, it is particularly difficult to single out any chapter above all others, as the entire text is a model of lucidity: if this is is not an example of a physics “classic”, then I am at a loss as to the definition of that term. Learn more regards: thermodynamic limit, efficacy of “completing-the-square,” (exercise, page 82), utility of “integration-by-parts ” (page 157), Gaussian approximation (page 177), probability distributions (page 226), left-and-right eigenvectors (page 255), and last, but not least, “the connection between renormalisation and dimensional analysis.” (page 306). Thus, the lectures come back almost full circle (introductory dimensional analysis culminating with the connections to renormalisation). Beautiful !This text gives one the impression of sitting-in on the Professor’s Lectures, being elated with that experience !Not an easy text by any stretch of the imagination, but dense with insight and “tricks-of-the-trade.”Highly Recommended.

⭐Nigel Goldenfeld’s book, “Lectures on Phase Transitions and the Renormalization Group” is clear, lucid, and very well-written. One of the most challenging things in writing such a book (I won’t call it a text; but it serves well for that purpose) is in helping the reader to gain conceptual insight into the subjects, and not to simply to present a series of equations. In this, Dr. Goldenfeld succeeds admirably.Topics that Goldenfeld discusses (most significantly; the renormalization group concept and critical phenomena) are presented in a very clear and accessible manner. In fact, his book is so useful that I have adopted his reference as my own “standard nomenclature,” and have translated my previously-used notation (and also studied in such classic’s as Hill’s “Statistical Mechanics”) to agree with Goldenfeld’s.One of the aspects that I am particularly enjoying is the care with which Goldenfeld builds the underlying logic and arguments as he approaches key points. This is very well-done, and makes this book a solid “go-to” reference in developing a well-grounded understanding of emerging yet very important topics.

⭐This is an excellent textbook for anyone who wants to learn how phase transition happens and the renormalization group. I think this will be the best introductory book if you want to learn about RG in the statistical mechanics context.

⭐The book at my hand is definitely a photocopy. Except that, it is a good book.

⭐This book was something I used to study Renormalization in my course in both undergrad and grad school. It is a classic, and I appreciated it far more after sitting through Nigel’s lectures on the same in class. Well written, well thought out and very pedagogical. Highly recommended.

⭐great book for anyone looking to understand some field theory.

⭐This book stands clearly to me as the best one on the vast and fascinating subject of phase transitions, critical phenomena and the renormalization group. My other references are Binney et al., Le Bellac and Yeomans. Nigel Goldenfeld’s course is the most suitable for a first contact with the field. It stresses in a exceptional way the ideas lying under each concept and has a gift for explaining what’s really going on beyond the equations. This can most clearly be seen with his careful discussion of ergodicity and symmetry breaking.Moreover, this book is remarkable in that it presents various openings on modern issues ; it includes an overview of disordered systems and a rather complete discussion of dynamical critical phenomena.After reading this book, you’ll probably be ready to fully appreciate the typical treaties on critical phenomena, which use more sharp technical tools but which require a good understanding of the associated physics you’ll only find so beautifully presented in Nigel Goldenfeld’s book.

⭐This books covers efficiently the basics of phase transitions and renormalization group, presenting and constructing them in a logical way, always with great care to the reasons and/or guesses according to which someone should actually try to do what is explained; in doing so, notes of caution on what could possibly go wrong are given.Footnotes often lead to more comprehensive or interesting references, providing a useful guide for the reader interested in the more gory details.By no means, as the preface states, a monography nor, in my own words, “the end of the story”, it provides with good physical reasonings and always tries to make the most sense.It’s probably not a really rigorous source on the subject, but for a first approach is both satisfactory and useful. For a more general approach from a pure field theory perspective, other books may be better suited to the task, but this remains a good source of physical understanding.The attentive reader will of course find errors, some, if I’m not mistaken, not listed in the errata corrige avalaible on the author’s webpage, but they are never fatal to the line of reasoning nor to understanding.There are a few instances of some notational confusion when treating renormalization group with adimensionalized variables, so I suggest to always check what you want to derive, what dimension it has and why, at the end, the result is the same in the case considered even if you “mess a bit”. It all turns out to be kind of a thermodynamics exercise.

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