FIELD THEORY, THE RENORMALIZATION GROUP, AND CRITICAL PHENOMENA: GRAPHS TO COMPUTERS (3RD EDITION)

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This book presents in a logical and consistent way the material that every budding condensed matter theorist should know on field theory before engaging in serious research.Within the first seven chapters, the authors derive the key results in euclidian field theory and lay the basis for further developments in renormalization theory and critical phenomena. That part of the book is almost self-contained and could serve as an alternative to the traditionally particle-physics oriented field theory course.Chapter 8 introduces properly the core concepts of any book on the subject, namely the renormalization group and critical phenomena. Once more, every technicalities are derived and no prior acquaintance to field theory is required (unlike in books like Itzykson & Drouffe two volumes). The major techniques, such as dimensional regularization, are nicely exposed. A salient point for using this course as a first introduction to quantum field theory would be that students would have a better feeling on the true meaning of renormalization and scale invariance than if those were presented in a particle physics context.Part II of this book exposes more specialized topics. The Coleman-Weinberg phenomenon and critical behaviour with several coupling constants are well presented. Crossover phenomena, critical phenomena in two dimensions have their respective chapters, too.Part III begins with real space renormalization methods ; here the presentation is a bit too formal, and returning to books like the one by Nigel Goldenfeld would improve the reader's appreciation of those methods.The book ends with some numerical recipes used in statistical field theory. Sample programs can be downloaded on a dedicated webpage.In short, an excellent, comprehensive, highly recommended textbook and reference work.

The book is well written, though very technical, I haven’t worked through the entire book, but very often I find myself having to scribble for two, three pages before being able to make the connection between two consecutive steps. But the content was nonetheless thoughtfully organized, precise and concise.The printing quality is however not so great. Though I haven’t encountered a single illegible word, the ink on one page sometimes is more faded than on others. The format of equations between paragraphs is also a bit strange, which is a minor inconvenience but hard to get used to it.

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