Field Theory, The Renormalization Group, And Critical Phenomena: Graphs To Computers (3rd Edition)
Field Theory, The Renormalization Group, And Critical Phenomena: Graphs To Computers (3rd Edition)

Author: Daniel J Amit

Publisher: World Scientific Publishing Company

Published: 2005-06-21

Total Pages: 568

ISBN-13: 9813102071

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This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. Non-perturbative methods and numerical simulations are introduced in this new edition. Abundant references to research literature complement this matter-of-fact approach. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.The following new chapters are included:I. Real Space MethodsII. Finite Size ScalingIII. Monte Carlo Methods. Numerical Field Theory

Field Theory, The Renormalization Group And Critical Phenomena (2nd Edition)
Field Theory, The Renormalization Group And Critical Phenomena (2nd Edition)

Author: Daniel J Amit

Publisher: World Scientific Publishing Company

Published: 1984-08-31

Total Pages: 412

ISBN-13: 9813104147

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This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.

The Theory of Critical Phenomena
The Theory of Critical Phenomena

Author: J. J. Binney

Publisher: Oxford University Press

Published: 1992-06-11

Total Pages: 477

ISBN-13: 0191660566

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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.

The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics
The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics

Author: A.N. Vasil'ev

Publisher: CRC Press

Published: 2004-04-28

Total Pages: 704

ISBN-13: 1134389663

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This volume provides a general field-theoretical picture of critical phenomena and stochastic dynamics and helps readers develop a practical skill for calculations. This education on the practical skill sets this book apart: it is the first to give a full technical introduction to the field. Both general ideas and ...hard... calculations are presen

Quantum Field Theory and Critical Phenomena
Quantum Field Theory and Critical Phenomena

Author: Jean Zinn-Justin

Publisher: Oxford University Press, USA

Published: 1993

Total Pages: 1034

ISBN-13:

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Describes particle physics and critical phenomena in statistical mechanics in a unified framework, incorporating graduate lecture notes from the 1970s and 1980s at several universities in Europe and the US. Deals with general field theory, functional integrals, and functional methods; renormalization properties of theories with symmetries and specific applications to particle physics; lattice gauge theories and asymptotic freedom in four dimensions; and the role of instantons and the application of instanton calculus to the large-order behavior of perturbation theory and the problem of summation of the perturbative expansion. Several chapters close with exercise, solutions or hints for which are provided. No dates are noted for the previous editions. Annotation copyright by Book News, Inc., Portland, OR

Quantum Field Theory and Critical Phenomena
Quantum Field Theory and Critical Phenomena

Author: Jean Zinn-Justin

Publisher: Oxford University Press

Published: 2021

Total Pages: 1074

ISBN-13: 0198834624

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Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamics has been the first example of a Quantum Field Theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. As this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, this text sets out to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group properties are systematically discussed. The notion of effective field theory and the emergence of renormalisable theories are described. The consequences for fine tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised, e.g. in particle physics with progress in neutrino physics and the discovery of the Higgs boson. The presentation has been made more homogeneous througout the volume, and emphasis has been put on the notion of effective field theory and discussion of the emergence of renormalisable theories.

Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory
Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory

Author: Roberto Fernandez

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 446

ISBN-13: 3662028662

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Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.

Elements of Phase Transitions and Critical Phenomena
Elements of Phase Transitions and Critical Phenomena

Author: Hidetoshi Nishimori

Publisher: Oxford University Press

Published: 2011

Total Pages: 373

ISBN-13: 0199577226

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As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.

Critical Dynamics
Critical Dynamics

Author: Uwe C. Täuber

Publisher: Cambridge University Press

Published: 2014-03-06

Total Pages: 529

ISBN-13: 0521842239

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A comprehensive and unified introduction to describing and understanding complex interacting systems.