Scaling and Renormalization in Statistical Physics (Cambridge Lecture Notes in Physics Book 5) 1st Edition by John Cardy (PDF)

Description

This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behaviour, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behaviour, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration, a selected bibliography, and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular, the perturbative method introduced leads, among other applications, to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting, avoiding the need for Feynman diagrams.

User’s Reviews

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

⭐I am a graduate student in condensed matter physics and I found this book to be an excellent introduction to the tools associated with the renormalization group idea. This book has a number of useful examples that are worked out in a fairly simple and straightforward way. In order to establish scaling relations this book uses some unit analysis on a hamiltonian density and builds from there. The one downside is that this book focuses on lowest order perturbation and doesn’t go into depth on diagrammatic approaches to renormalization ideas. Aside from this it is a great reference and many of my colleagues swear by it.

⭐This book deals with a most interesting and dynamical area of modern research in physics.In the frontmatters, Cardy explains that, too often, in the past, students who were willing to go into research in condensed matter as quickly as possible, found a difficult time struggling and mastering techniques that were initially devised for particule physics.K. Wilson built an arch between these two sub-fields of physics, through his Nobel-prize-worth insights.However, as Cardy rightly points out, renormalization group methods can be more efficiently explained, learnt and applied by condensed matter, in a Feynman-diagram inspired presentation of the perturbative renormalization group. This subject then reduce to relatively simple combinatorics.This is one of this book main contribution.After explaining carefully scaling concepts and the various corresponding laws of critical phenomena, as well as field theory and Landau-Ginzburg theory, Cardy goes on to explain those from renormalization group methods.The usual (exactly solved) statistical models appear at various parts of the book.Welcome additions to the literature are chapters on random systems (those with impureties), polymer physics and critical dynamics.A final chapter offers a primer on how conformal symmetry pops out at the critical point. This is a most active subject of current research in the field.I should stress however that this book is meant for advanced students.The typical student would have a background in phase transitions and statistical physics, as well as prior acquaintance with basic (quantum)field theory.This book would probably be more profitably read with a more experienced student or a teacher at hand, for it is written in a rather condensed form and due to the vastness of the subject can hardly give an overview of it.

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