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A Primer To The Theory Of Critical Phenomena

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A Primer to the Theory of Critical Phenomena

A Primer to the Theory of Critical Phenomena Book
Author : Jurgen M. Honig,Jozef Spalek
Publisher : Elsevier
Release : 2018-02-05
ISBN : 0128048360
Language : En, Es, Fr & De

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Book Description :

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

Introduction to the Theory of Critical Phenomena

Introduction to the Theory of Critical Phenomena Book
Author : D. I. Uzunov
Publisher : World Scientific
Release : 1993
ISBN : 9789810203887
Language : En, Es, Fr & De

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Book Description :

The sophistication of modern tools used in the study of statistical mechanics and field theory is often an obstacle to the easy understanding of new important current results reported in journals. The main purpose of this book is to introduce the reader to the methods of the fluctuation (field) theory of phase transitions and critical phenomena so as to provide a good source for research. The introductory contents are concerned with ideas of description, thermodynamic stability theory related to phase transitions, major experimental facts, basic models and their relationships. Special attention is paid to the mean field approximation and to the Landau expansion for simple and complex models of critical and multicritical phenomena. An instructive representation of the modern perturbation theory and the method of the renormalization group is developed for field models of phase transitions. The essential influence of the fluctuations on the critical behaviour is established together with the theory of correlation functions, Gaussian approximation, the Ginzburg criterion, ?- and 1/n- expansions as practical realizations of the renormalization group ideas. Applications of the theory to concrete aspects of condensed matter physics are considered: quantum effects, Bose condensation, crystal anisotropy, superconductors and liquid crystals, effects of disorder of type randomly distributed quenched impurities and random fields. This volume can be used as an advanced University course book for students with a basic knowledge of statistical physics and quantum mechanics. It could be considered as a complementary text to a standard University course on statistical physics.

A Primer for Chiral Perturbation Theory

A Primer for Chiral Perturbation Theory Book
Author : Stefan Scherer,Matthias R. Schindler
Publisher : Springer Science & Business Media
Release : 2011-10-02
ISBN : 364219253X
Language : En, Es, Fr & De

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Book Description :

Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques.

Critical Properties of Phi4 Theories

Critical Properties of Phi4 Theories Book
Author : Hagen Kleinert,Verena Schulte-Frohlinde
Publisher : World Scientific
Release : 2001-07-30
ISBN : 9814490792
Language : En, Es, Fr & De

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Book Description :

This book explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition. Beginning with an introduction to critical phenomena, this book develops the functional-integral description of quantum field theories, their perturbation expansions, and a method for finding recursively all Feynman diagrams to any order in the coupling strength. Algebraic computer programs are supplied on accompanying World Wide Web pages. The diagrams correspond to integrals in momentum space. They are evaluated in 4-ε dimensions, where they possess pole terms in 1/ε. The pole terms are collected into renormalization constants. The theory of the renormalization group is used to find the critical scaling laws. They contain critical exponents which are obtained from the renormalization constants in the form of power series. These are divergent, due to factorially growing expansion coefficients. The evaluation requires resummation procedures, which are performed in two ways: (1) using traditional methods based on Padé and Borel transformations, combined with analytic mappings; (2) using modern variational perturbation theory, where the results follow from a simple strong-coupling formula. As a crucial test of the accuracy of the methods, the critical exponent α governing the divergence of the specific heat of superfluid helium is shown to agree very well with the extremely precise experimental number found in the space shuttle orbiting the earth (whose data are displayed on the cover of the book). The phi4-theories investigated in this book contain any number N of fields in an O(N)-symmetric interaction, or in an interaction in which O(N)-symmetry is broken by a term of a cubic symmetry. The crossover behavior between the different symmetries is investigated. In addition, alternative ways of obtaining critical exponents of phi4-theories are sketched, such as variational perturbation expansions in three rather than 4-ε dimensions, and improved ratio tests in high-temperature expansions of lattice models. Contents:Definition of phi4-TheoryFeynman DiagramsDiagrams in Momentum SpaceStructural Properties of Perturbation TheoryDiagrams for Multicomponent FieldsScale Transformations of Fields and Correlation FunctionsRegularization of Feynman IntegralsRenormalizationRenormalization GroupRecursive Subtraction of UV-Divergences via R-OperationZero-Mass Approach to CountertermsCalculation of Momentum Space IntegralsGeneration of DiagramsResults of the Five-Loop CalculationBasic Resummation TheoryCritical Exponents of O(N)-Symmetric TheoryCubic AnisotropyVariational Perturbation TheoryCritical Exponents from Other ExpansionsNew Resummation AlgorithmConclusion:Diagrammatic R-Operation Up to Five LoopsContributions to Renormalization-Constants Readership: Graduate students, researchers and academics/lecturers in theoretical physics. Keywords:Reviews:“This book is overall a very good one on the RG as applied to critical phenomena. I believe that it will soon achieve the status of a standard reference book on this subject.”Journal of Statistical Physics

Critical Properties of Greek Letter Phi 4 theories

Critical Properties of  Greek Letter Phi 4 theories Book
Author : Hagen Kleinert,Verena Schulte-Frohlinde
Publisher : World Scientific Publishing Company Incorporated
Release : 2001
ISBN : 9789810246587
Language : En, Es, Fr & De

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Book Description :

Based upon lecture notes for a course taught by Kleinert, this monograph explains in detail how to perform perturbation expansions in quantum field theory to high orders. The authors also describe how to extract the critical properties of the theory from the resulting divergent power series. Kleinert teaches physics at the Freie U. in Berlin and Schulte-Frohlinde is a visiting scientist at Harvard. Annotation copyrighted by Book News Inc., Portland, OR.

Quantum Field Theory and Critical Phenomena

Quantum Field Theory and Critical Phenomena Book
Author : Jean Zinn-Justin,Cea/Saclay Service de Physique Theorique Jean Zinn-Justin
Publisher : Oxford University Press
Release : 1996
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Over the last twenty years quantum field theory has become not only the framework for the discussion of all fundamental interactions except gravity, but also for the understanding of second-order phase transitions in statistical mechanics.This advanced text is based on graduate courses and summer schools given by the author over a number of years. It approaches the subject in terms of path and functional intergrals, adopting a Euclidean metric and using the language of partition and correlation functions. Renormalization and therenormalization group are examined, as are critical phenomena and the role of instantons.Changes for this edition1. Extensive revision to eliminate a few bugs that had survived the second edition and (mainly) to improve the pedagogical presentation, as a result of experience gathered by lecturing.2. Additional new topics; holomorphic or coherent state path integral; functional integral and representation of the field theory S-matrix in the holomorphic formalis; non-relativistic limit of massive quantization and brief discussion of non-renormalization of quantum gravity based on Einsteinaction.3. Finally 65 pages of solutions or hints of solutions to the exercises at the ends of chapters.

Critical Dynamics

Critical Dynamics Book
Author : Uwe C. Täuber
Publisher : Cambridge University Press
Release : 2014-03-06
ISBN : 1139867202
Language : En, Es, Fr & De

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Book Description :

Introducing a unified framework for describing and understanding complex interacting systems common in physics, chemistry, biology, ecology, and the social sciences, this comprehensive overview of dynamic critical phenomena covers the description of systems at thermal equilibrium, quantum systems, and non-equilibrium systems. Powerful mathematical techniques for dealing with complex dynamic systems are carefully introduced, including field-theoretic tools and the perturbative dynamical renormalization group approach, rapidly building up a mathematical toolbox of relevant skills. Heuristic and qualitative arguments outlining the essential theory behind each type of system are introduced at the start of each chapter, alongside real-world numerical and experimental data, firmly linking new mathematical techniques to their practical applications. Each chapter is supported by carefully tailored problems for solution, and comprehensive suggestions for further reading, making this an excellent introduction to critical dynamics for graduate students and researchers across many disciplines within physical and life sciences.

Thermodynamics

Thermodynamics Book
Author : Jurgen M. Honig
Publisher : Academic Press
Release : 2020-11-07
ISBN : 0128233699
Language : En, Es, Fr & De

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Book Description :

Thermodynamics: Principles Characterizing Physical and Chemical Processes, Fifth Edition is an authoritative guide on the physical and chemical processes based on classical thermodynamic principles. Emphasis is placed on fundamental principles, with a combination of theory and practice that demonstrates their applications in a variety of disciplines. Revised and updated to include new material and novel formulations, this edition features a new chapter on algebraic power laws and Fisher information theory, along with detailed updates on irreversible phenomena, Landau theory, self-assembly, Caratheodory’s theorem, and the effects of externally applied fields. Drawing on the experience of its expert author, this book is a useful tool for both graduate students, professional chemists, and physicists who wish to acquire a more sophisticated overview of thermodynamics and related subject matter. Updated to reflect the latest developments in the field, including a new chapter on algebraic power laws and Fisher information theory Includes clear explanations of abstract theoretical concepts Provides exhaustive coverage of graphical, numerical and analytical computational techniques

Ageing and the Glass Transition

Ageing and the Glass Transition Book
Author : Malte Henkel,Michel Pleimling,Roland Sanctuary
Publisher : Springer Science & Business Media
Release : 2007-04-24
ISBN : 3540696830
Language : En, Es, Fr & De

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Book Description :

Understanding cooperative phenomena far from equilibrium is one of the fascinating challenges of present-day many-body physics. Glassy behaviour and the physical ageing process of such materials are paradigmatic examples. The present volume, primarily intended as introduction and reference, collects six extensive lectures addressing selected experimental and theoretical issues in the field of glassy systems.

Percolation Theory and Ergodic Theory of Infinite Particle Systems

Percolation Theory and Ergodic Theory of Infinite Particle Systems Book
Author : Harry Kesten
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461387345
Language : En, Es, Fr & De

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Book Description :

This IMA Volume in ~athematics and its Applications PERCOLATION THEORY AND ERGODIC THEORY OF INFINITE PARTICLE SYSTEMS represents the proceedings of a workshop which was an integral part of the 19R4-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: naniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaoo for planning and implementing an exciting and stimulating year-long program. We especially thank the Workshop Organizing Committee, Harry Kesten (Chairman), Richard Holley, and Thomas Liggett for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinherger PREFACE Percolation theory and interacting particle systems both have seen an explosive growth in the last decade. These suhfields of probability theory are closely related to statistical mechanics and many of the publications on these suhjects (especially on the former) appear in physics journals, wit~ a great variahility in the level of rigour. There is a certain similarity and overlap hetween the methods used in these two areas and, not surprisingly, they tend to attract the same probabilists. It seemed a good idea to organize a workshop on "Percolation Theory and Ergodic Theory of Infinite Particle Systems" in the framework of the special probahility year at the Institute for Mathematics and its Applications in 1985-86. Such a workshop, dealing largely with rigorous results, was indeed held in February 1986.

Quantum Field Theory in Condensed Matter Physics

Quantum Field Theory in Condensed Matter Physics Book
Author : Naoto Nagaosa
Publisher : Springer Science & Business Media
Release : 2013-11-11
ISBN : 3662037742
Language : En, Es, Fr & De

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Book Description :

This is an approachable introduction to the important topics and recent developments in the field of condensed matter physics. First, the general language of quantum field theory is developed in a way appropriate for dealing with systems having a large number of degrees of freedom. This paves the way for a description of the basic processes in such systems. Applications include various aspects of superfluidity and superconductivity, as well as a detailed description of the fractional quantum Hall liquid.

Ginzburg Landau Theory of Condensates

Ginzburg   Landau Theory of Condensates Book
Author : Baruch Rosenstein,Dingping Li
Publisher : Cambridge University Press
Release : 2021-11-30
ISBN : 1108836852
Language : En, Es, Fr & De

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Book Description :

A primer on Ginzberg-Landau Theory considering common and topological excitations including their thermodynamics and dynamical phenomena.

Critical Phenomena in Natural Sciences

Critical Phenomena in Natural Sciences Book
Author : Didier Sornette
Publisher : Springer Science & Business Media
Release : 2013-04-17
ISBN : 366204174X
Language : En, Es, Fr & De

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Book Description :

A modern up-to-date introduction for readers outside statistical physics. It puts emphasis on a clear understanding of concepts and methods and provides the tools that can be of immediate use in applications.

Quantum Field Theory

Quantum Field Theory Book
Author : Michael V. Sadovskii
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2019-05-20
ISBN : 3110648520
Language : En, Es, Fr & De

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Book Description :

This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The theoretical results are derived using the physical phenomena as a starting point. This inductive approach allows a deep understanding of the methods used for solving problems in this field. This second, revised edition is expanded with biographical notes contextualizing the main results in quantum field theory.

Many Body Problems and Quantum Field Theory

Many Body Problems and Quantum Field Theory Book
Author : Philippe Andre Martin,Francois Rothen
Publisher : Springer Science & Business Media
Release : 2013-11-11
ISBN : 3662048949
Language : En, Es, Fr & De

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Book Description :

Emphasis is placed on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas within different domains of physics. Starting from a basic knowledge of quantum mechanics and classical electromagnetism, the exposition is self-contained and explicitly details all steps of the derivations. The new edition features a substantially new treatment of nucleon pairing.

Recent Studies inPerturbation Theory

Recent Studies inPerturbation Theory Book
Author : Dimo Uzunov
Publisher : BoD – Books on Demand
Release : 2017-06-14
ISBN : 953513261X
Language : En, Es, Fr & De

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Book Description :

The book contains seven chapters written by noted experts and young researchers who present their recent studies of both pure mathematical problems of perturbation theories and application of perturbation methods to the study of the important topic in physics, for example, renormalization group theory and applications to basic models in theoretical physics (Y. Takashi), the quantum gravity and its detection and measurement (F. Bulnes), atom-photon interactions (E. G. Thrapsaniotis), treatment of spectra and radiation characteristics by relativistic perturbation theory (A. V. Glushkov et al), and Green's function theory and some applications (Jing Huang). The pure mathematical issues are related to the problem of generalization of the boundary layer function method for bisingularly perturbed differential equations (K. Alymkulov and D. A. Torsunov) and to the development of new homotopy asymptotic methods and some of their applications (Baojian Hong).

Semiclassical and Stochastic Gravity

Semiclassical and Stochastic Gravity Book
Author : Bei-Lok B. Hu,Enric Verdaguer
Publisher : Cambridge University Press
Release : 2020-02-29
ISBN : 1108854141
Language : En, Es, Fr & De

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Book Description :

The two pillars of modern physics are general relativity and quantum field theory, the former describes the large scale structure and dynamics of space-time, the latter, the microscopic constituents of matter. Combining the two yields quantum field theory in curved space-time, which is needed to understand quantum field processes in the early universe and black holes, such as the well-known Hawking effect. This book examines the effects of quantum field processes back-reacting on the background space-time which become important near the Planck time (10-43 sec). It explores the self-consistent description of both space-time and matter via the semiclassical Einstein equation of semiclassical gravity theory, exemplified by the inflationary cosmology, and fluctuations of quantum fields which underpin stochastic gravity, necessary for the description of metric fluctuations (space-time foams). Covering over four decades of thematic development, this book is a valuable resource for researchers interested in quantum field theory, gravitation and cosmology.