Introduction To Renormalization Group Methods In Physics

Author : Richard J. Creswick,Horacio A. Farach,Charles P. Poole
Publisher : Wiley-Interscience
Page : 432 pages
File Size : 51,5 Mb
Release : 1992
Category : Science
ISBN : UOM:39076001138036

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Introduction to Renormalization Group Methods in Physics by Richard J. Creswick,Horacio A. Farach,Charles P. Poole Pdf

The renormalization group (RG) method has found applications in many areas of physics. The authors present simple RG treatments of such diverse problems as random walks, percolation, chaos and critical phenomena. Detailed introductory materials are presented in each area which makes it reasonably self–contained. The concepts of self–similarity and scale invariance are a common thread tying these problems together. Emphasis is placed on intuitive real–space RG calculations rather than formalism. The momentum–space RG is introduced and the 1/n and epsis expansions are discussed. A brief explanation of the field–theoretic approach to the RG serves as an introduction to more advanced techniques.

Author : Roland Bauerschmidt,David C. Brydges,Gordon Slade
Publisher : Springer Nature
Page : 283 pages
File Size : 43,6 Mb
Release : 2019-10-16
Category : Science
ISBN : 9789813295933

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Introduction to a Renormalisation Group Method by Roland Bauerschmidt,David C. Brydges,Gordon Slade Pdf

This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.

Author : J. J. Binney,N. J. Dowrick,A. J. Fisher,M. E. J. Newman
Publisher : Oxford University Press
Page : 477 pages
File Size : 51,8 Mb
Release : 1992-06-11
Category : Science
ISBN : 9780191660566

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The Theory of Critical Phenomena by J. J. Binney,N. J. Dowrick,A. J. Fisher,M. E. J. Newman Pdf

The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.

Author : John Clements Collins
Publisher : Cambridge University Press
Page : 396 pages
File Size : 49,9 Mb
Release : 1984
Category : Science
ISBN : 0521311772

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Renormalization by John Clements Collins Pdf

This book provides a coherent exposition of the techniques underlying these calculations.

Author : Dimo I. Uzunov
Publisher : World Scientific
Page : 701 pages
File Size : 44,7 Mb
Release : 2010
Category : Science
ISBN : 9789814299497

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Introduction to the Theory of Critical Phenomena by Dimo I. Uzunov Pdf

This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.

Author : Dimo I Uzunov
Publisher : World Scientific Publishing Company
Page : 700 pages
File Size : 55,6 Mb
Release : 2010-08-31
Category : Science
ISBN : 9789813100909

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Introduction to the Theory of Critical Phenomena by Dimo I Uzunov Pdf

This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.

Author : Manfred Salmhofer
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 53,8 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662038734

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Renormalization by Manfred Salmhofer Pdf

This monograph is the first to present the recently discovered renormalization techniques for the Schrödinger and Dirac equations, providing a mathematically rigorous, yet simple and clear introduction to the subject. It develops field-theoretic techniques such as Feynman graph expansions and renormalization, taking pains to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is performed by using an exact renormalization group differential equation, a technique that provides simple but complete proofs of the theorems.

Author : Giuseppe Benfatto,Giovanni Gallavotti
Publisher : Princeton University Press
Page : 156 pages
File Size : 43,7 Mb
Release : 2020-11-10
Category : Science
ISBN : 9780691221694

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Renormalization Group by Giuseppe Benfatto,Giovanni Gallavotti Pdf

Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems. The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties.

Author : John C. Collins
Publisher : Cambridge University Press
Page : 393 pages
File Size : 42,5 Mb
Release : 2023-07-31
Category : Science
ISBN : 9781009401760

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Renormalization by John C. Collins Pdf

Author : Peter Kopietz,Lorenz Bartosch,Florian Schütz
Publisher : Springer
Page : 380 pages
File Size : 47,8 Mb
Release : 2010-04-22
Category : Science
ISBN : 9783642050947

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Introduction to the Functional Renormalization Group by Peter Kopietz,Lorenz Bartosch,Florian Schütz Pdf

The renormalization group (RG) has nowadays achieved the status of a meta-theory, which is a theory about theories. The theory of the RG consists of a set of concepts and methods which can be used to understand phenomena in many different ?elds of physics, ranging from quantum ?eld theory over classical statistical mechanics to nonequilibrium phenomena. RG methods are particularly useful to understand phenomena where ?uctuations involving many different length or time scales lead to the emergence of new collective behavior in complex many-body systems. In view of the diversity of ?elds where RG methods have been successfully applied, it is not surprising that a variety of apparently different implementations of the RG idea have been proposed. Unfortunately, this makes it somewhat dif?cult for beginners to learn this technique. For example, the ?eld-theoretical formulation of the RG idea looks at the ?rst sight rather different from the RG approach pioneered by Wilson, the latter being based on the concept of the effective action which is ite- tively calculated by successive elimination of the high-energy degrees of freedom. Moreover, the Wilsonian RG idea has been implemented in many different ways, depending on the particular problem at hand, and there seems to be no canonical way of setting up the RG procedure for a given problem.

Author : Peter Kopietz,Lorenz Bartosch,Florian Schütz
Publisher : Springer Science & Business Media
Page : 383 pages
File Size : 48,9 Mb
Release : 2010-05-03
Category : Language Arts & Disciplines
ISBN : 9783642050930

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Introduction to the Functional Renormalization Group by Peter Kopietz,Lorenz Bartosch,Florian Schütz Pdf

This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.

Author : Achim Schwenk,Janos Polonyi
Publisher : Springer
Page : 356 pages
File Size : 52,9 Mb
Release : 2012-06-25
Category : Science
ISBN : 9783642273209

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Renormalization Group and Effective Field Theory Approaches to Many-Body Systems by Achim Schwenk,Janos Polonyi Pdf

There have been many recent and important developments based on effective field theory and the renormalization group in atomic, condensed matter, nuclear and high-energy physics. These powerful and versatile methods provide novel approaches to study complex and strongly interacting many-body systems in a controlled manner. The six extensive lectures gathered in this volume combine selected introductory and interdisciplinary presentations focused on recent applications of effective field theory and the renormalization group to many-body problems in such diverse fields as BEC, DFT, extreme matter, Fermi-liquid theory and gauge theories. Primarily aimed at graduate students and junior researchers, they offer an opportunity to explore fundamental physics across subfield boundaries at an early stage in their careers.

Author : John Cardy
Publisher : Cambridge University Press
Page : 264 pages
File Size : 51,7 Mb
Release : 1996-04-26
Category : Science
ISBN : 0521499593

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Scaling and Renormalization in Statistical Physics by John Cardy Pdf

This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.

Author : W. D. McComb
Publisher : Oxford University Press
Page : 349 pages
File Size : 43,7 Mb
Release : 2004
Category : Business & Economics
ISBN : 9780198506942

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Renormalization Methods by W. D. McComb Pdf

This text fills a gap between undergraduate and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation, proceeds to the epsilon-expansion and ends with the first-order corrections to critical exponents beyond mean-field theory.

Author : Nigel Goldenfeld
Publisher : CRC Press
Page : 417 pages
File Size : 45,9 Mb
Release : 2018-03-08
Category : Science
ISBN : 9780429962042

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Lectures On Phase Transitions And The Renormalization Group by Nigel Goldenfeld Pdf

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.