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A Primer to the Theory of Critical Phenomena by Jurgen M. Honig,Jozef Spalek Pdf
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
Modern Theory Of Critical Phenomena by Shang-keng Ma Pdf
An important contributor to our current understanding of critical phenomena, Ma introduces the beginner--especially the graduate student with no previous knowledge of the subject-to fundamental theoretical concepts such as mean field theory, the scaling hypothesis, and the renormalization group. He then goes on to apply the renormalization group to selected problems, with emphasis on the underlying physics and the basic assumptions involved.
Soft Matter by Wim van Saarloos,Vincenzo Vitelli,Zorana Zeravcic Pdf
"Soft matter science is an interdisciplinary field at the interface of physics, biology, chemistry, engineering, and materials science. It encompasses colloids, polymers, and liquid crystals as well as rapidly emerging topics such as metamaterials, memory formation and learning in matter, bioactive systems, and artificial life. This textbook introduces key phenomena and concepts in soft matter from a modern perspective, marrying established knowledge with the latest developments and applications. The presentation integrates statistical mechanics, dynamical systems, and hydrodynamic approaches, emphasizing conservation laws and broken symmetries as guiding principles while paying attention to computational and machine learning advances. The book features introductory chapters on fluid mechanics, elasticity, and stochastic phenomena and also covers advanced topics such as pattern formation and active matter. it discusses technological applications as well as relevant phenomena in the life sciences and offers perspectives on emerging research directions"--
Critical Properties of Phi4-Theories by Hagen Kleinert,Verena Schulte-Frohlinde Pdf
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
Statistical Field Theory: Volume 2, Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems by Claude Itzykson,Jean-Michel Drouffe Pdf
Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.
Critical Properties of [Greek Letter Phi]4-theories by Hagen Kleinert,Verena Schulte-Frohlinde Pdf
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-î dimensions, where they possess pole terms in 1/î. 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 Pad 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 à 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-î dimensions, and improved ratio tests in high-temperature expansions of lattice models.
Quantum Field Theory and Critical Phenomena by Jean Zinn-Justin Pdf
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.
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 by Malte Henkel,Michel Pleimling,Roland Sanctuary Pdf
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 by Harry Kesten Pdf
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 by Naoto Nagaosa Pdf
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.
Author : Michael V. Sadovskii Publisher : Walter de Gruyter GmbH & Co KG Page : 443 pages File Size : 48,9 Mb Release : 2019-05-20 Category : Science ISBN : 9783110648522
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.
A Primer on Critical Thinking and Business Ethics by Oswald A. J. Mascarenhas, SJ,Munish Thakur,Payal Kumar Pdf
Encapsulating new developments in Critical Thinking skills for MBA students, in the form of a broad-based cross disciplinary primer in business management, with a special focus on business ethics.
