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.


Scaling and Renormalization in Statistical Physics

Scaling and Renormalization in Statistical Physics

Author: John Cardy

Publisher: Cambridge University Press

Published: 1996-04-26

Total Pages: 264

ISBN-13: 9780521499590

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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.


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.


A Modern Approach to Critical Phenomena

A Modern Approach to Critical Phenomena

Author: Igor Herbut

Publisher: Cambridge University Press

Published: 2007-01-04

Total Pages: 223

ISBN-13: 1139460129

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Critical phenomena is one of the most exciting areas of modern physics. This 2007 book provides a thorough but economic introduction into the principles and techniques of the theory of critical phenomena and the renormalization group, from the perspective of modern condensed matter physics. Assuming basic knowledge of quantum and statistical mechanics, the book discusses phase transitions in magnets, superfluids, superconductors, and gauge field theories. Particular attention is given to topics such as gauge field fluctuations in superconductors, the Kosterlitz-Thouless transition, duality transformations, and quantum phase transitions - all of which are at the forefront of physics research. This book contains numerous problems of varying degrees of difficulty, with solutions. These problems provide readers with a wealth of material to test their understanding of the subject. It is ideal for graduate students and more experienced researchers in the fields of condensed matter physics, statistical physics, and many-body physics.


Introduction to the Functional Renormalization Group

Introduction to the Functional Renormalization Group

Author: Peter Kopietz

Publisher: Springer Science & Business Media

Published: 2010-05-03

Total Pages: 383

ISBN-13: 364205093X

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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.


Renormalization Methods

Renormalization Methods

Author: W. D. McComb

Publisher: Oxford University Press

Published: 2004

Total Pages: 349

ISBN-13: 0198506945

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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.


Non-Equilibrium Phase Transitions

Non-Equilibrium Phase Transitions

Author: Malte Henkel

Publisher: Springer Science & Business Media

Published: 2008-11-27

Total Pages: 385

ISBN-13: 1402087659

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This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.


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.


Statistical Physics of Fields

Statistical Physics of Fields

Author: Mehran Kardar

Publisher: Cambridge University Press

Published: 2007-06-07

Total Pages: 376

ISBN-13: 1139855883

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While many scientists are familiar with fractals, fewer are familiar with scale-invariance and universality which underlie the ubiquity of their shapes. These properties may emerge from the collective behaviour of simple fundamental constituents, and are studied using statistical field theories. Initial chapters connect the particulate perspective developed in the companion volume, to the coarse grained statistical fields studied here. Based on lectures taught by Professor Kardar at MIT, this textbook demonstrates how such theories are formulated and studied. Perturbation theory, exact solutions, renormalization groups, and other tools are employed to demonstrate the emergence of scale invariance and universality, and the non-equilibrium dynamics of interfaces and directed paths in random media are discussed. Ideal for advanced graduate courses in statistical physics, it contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set available to lecturers at www.cambridge.org/9780521873413.


A Primer to the Theory of Critical Phenomena

A Primer to the Theory of Critical Phenomena

Author: Jurgen M. Honig

Publisher: Elsevier

Published: 2018-02-05

Total Pages: 256

ISBN-13: 0128048360

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A Primer to the Theory of Critical Phenomena provides scientists in academia and industry, as well as graduate students in physics, chemistry, and geochemistry with the scientific fundamentals of critical phenomena and phase transitions. The book helps readers broaden their understanding of a field that has developed tremendously over the last forty years. The book also makes a great resource for graduate level instructors at universities. - Provides a thorough and accessible treatment of the fundamentals of critical phenomena - Offers an in-depth exposition on renormalization and field theory techniques - Includes experimental observations of critical effects - Includes live examples illustrating the applications of the theoretical material