Download or read book Introduction To The Theory Of Critical Phenomena Mean Field Fluctuations And Renormalization 2nd Edition written by Dimo I Uzunov and published by World Scientific Publishing Company. This book was released on 2010-08-31 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Theory of Critical Phenomena written by J. J. Binney and published by Oxford University Press. This book was released on 1992-06-11 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Primer to the Theory of Critical Phenomena written by Jurgen M. Honig and published by Elsevier. This book was released on 2018-02-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Critical Dynamics written by Uwe C. Täuber and published by Cambridge University Press. This book was released on 2014-03-06 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Field Theory The Renormalization Group And Critical Phenomena 2nd Edition written by Daniel J Amit and published by World Scientific Publishing Company. This book was released on 1984-08-31 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Order Disorder And Criticality Advanced Problems Of Phase Transition Theory Volume 2 written by Yurij Holovatch and published by World Scientific. This book was released on 2007-07-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second volume of review papers on advanced problems of phase transitions and critical phenomena, following the success of the first volume in 2004. Broadly, the volume aims to demonstrate that the phase transition theory, which experienced its 'golden age' during the 70s and 80s, is far from over and there is still a good deal of work to be done, both at the fundamental level and in respect of applications.The topics presented in this volume include: critical behavior as explained by the non-perturbative renormalization group, critical dynamics, a spacetime approach to phase transitions, self-organized criticality, and exactly solvable models of phase transitions in strongly correlated systems. As the first volume, this book is based on the review lectures that were given in Lviv (Ukraine) at the “Ising lectures” — a traditional annual workshop on phase transitions and critical phenomena which brings together scientists working in the field with university students and those who are interested in the subject.
Download or read book The Mathematics of Urban Morphology written by Luca D'Acci and published by Springer. This book was released on 2019-03-23 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume provides an essential resource for urban morphology, the study of urban forms and structures, offering a much-needed mathematical perspective. Experts on a variety of mathematical modeling techniques provide new insights into specific aspects of the field, such as street networks, sustainability, and urban growth. The chapters collected here make a clear case for the importance of tools and methods to understand, model, and simulate the formation and evolution of cities. The chapters cover a wide variety of topics in urban morphology, and are conveniently organized by their mathematical principles. The first part covers fractals and focuses on how self-similar structures sort themselves out through competition. This is followed by a section on cellular automata, and includes chapters exploring how they generate fractal forms. Networks are the focus of the third part, which includes street networks and other forms as well. Chapters that examine complexity and its relation to urban structures are in part four.The fifth part introduces a variety of other quantitative models that can be used to study urban morphology. In the book’s final section, a series of multidisciplinary commentaries offers readers new ways of looking at the relationship between mathematics and urban forms. Being the first book on this topic, Mathematics of Urban Morphology will be an invaluable resource for applied mathematicians and anyone studying urban morphology. Additionally, anyone who is interested in cities from the angle of economics, sociology, architecture, or geography will also find it useful. "This book provides a useful perspective on the state of the art with respect to urban morphology in general and mathematics as tools and frames to disentangle the ideas that pervade arguments about form and function in particular. There is much to absorb in the pages that follow and there are many pointers to ways in which these ideas can be linked to related theories of cities, urban design and urban policy analysis as well as new movements such as the role of computation in cities and the idea of the smart city. Much food for thought. Read on, digest, enjoy." From the foreword by Michael Batty
Download or read book A Modern Approach to Critical Phenomena written by Igor Herbut and published by Cambridge University Press. This book was released on 2007-01-04 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Liquid Crystals and Their Computer Simulations written by Claudio Zannoni and published by Cambridge University Press. This book was released on 2022-07-31 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Standing as the first unified textbook on the subject, Liquid Crystals and Their Computer Simulations provides a comprehensive and up-to-date treatment of liquid crystals and of their Monte Carlo and molecular dynamics computer simulations. Liquid crystals have a complex physical nature, and, therefore, computer simulations are a key element of research in this field. This modern text develops a uniform formalism for addressing various spectroscopic techniques and other experimental methods for studying phase transitions of liquid crystals, and emphasises the links between their molecular organisation and observable static and dynamic properties. Aided by the inclusion of a set of Appendices containing detailed mathematical background and derivations, this book is accessible to a broad and multidisciplinary audience. Primarily intended for graduate students and academic researchers, it is also an invaluable reference for industrial researchers working on the development of liquid crystal display technology.
Download or read book Physics of Critical Fluctuations written by Yuli M. Ivanchenko and published by Springer Science & Business Media. This book was released on 1995-09-21 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on Wilson's renormalization group, the authors have developed a unified approach that not only reproduces known results but also yields new results. A systematic exposition of the contemporary theory of phase transitions, the book includes detailed discussions of phenomena in Heisenberg magnets, granular super-conducting alloys, anisotropic systems of dipoles, and liquid-vapor transitions. Suitable for advanced undergraduates as well as graduate students in physics, the text assumes some knowledge of statistical mechanics, but is otherwise self-contained.
Download or read book Coherent Anomaly Method written by Masuo Suzuki and published by World Scientific. This book was released on 1995 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic and coherent approach to phase transitions and critical phenomena, namely the coherent-anomaly method (CAM theory) based on cluster mean-field approximations. The first part gives a brief review of the CAM theory and the second part a collection of reprints covering the CAM basic calculations, the Blume-Emery-Griffiths model, the extended Baxter model, the quantum Heisenberg model, zero-temperature phase transitions, the KT-transition, spin glasses, the self-avoiding walk, contact processes, branching processes, the gas-liquid transition and even non-equilibrium phase transitions.
Download or read book Elements of Phase Transitions and Critical Phenomena written by Hidetoshi Nishimori and published by Oxford University Press. This book was released on 2011 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book CERN Courier written by and published by . This book was released on 2011 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Mechanics of Phase Transitions written by J. M. Yeomans and published by Clarendon Press. This book was released on 1992-05-07 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to the physics which underlies phase transitions and to the theoretical techniques currently at our disposal for understanding them. It will be useful for advanced undergraduates, for post-graduate students undertaking research in related fields, and for established researchers in experimental physics, chemistry, and metallurgy as an exposition of current theoretical understanding. - ;Recent developments have led to a good understanding of universality; why phase transitions in systems as diverse as magnets, fluids, liquid crystals, and superconductors can be brought under the same theoretical umbrella and well described by simple models. This book describes the physics underlying universality and then lays out the theoretical approaches now available for studying phase transitions. Traditional techniques, mean-field theory, series expansions, and the transfer matrix, are described; the Monte Carlo method is covered, and two chapters are devoted to the renormalization group, which led to a break-through in the field. The book will be useful as a textbook for a course in `Phase Transitions', as an introduction for graduate students undertaking research in related fields, and as an overview for scientists in other disciplines who work with phase transitions but who are not aware of the current tools in the armoury of the theoretical physicist. - ;Introduction; Statistical mechanics and thermodynamics; Models; Mean-field theories; The transfer matrix; Series expansions; Monte Carlo simulations; The renormalization group; Implementations of the renormalization group. -
Download or read book Principles of Condensed Matter Physics written by P. M. Chaikin and published by Cambridge University Press. This book was released on 2000-09-28 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: This successful and widely-reviewed book covering the physics of condensed matter systems is now available in paperback.
Download or read book Critical Properties of Greek Letter Phi 4 theories written by Hagen Kleinert and published by World Scientific. This book was released on 2001 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fundamentals of Condensed Matter and Crystalline Physics written by David L. Sidebottom and published by Cambridge University Press. This book was released on 2012-07-05 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook merges traditional solid state physics with contemporary condensed matter physics, providing an up-to-date introduction to the major concepts that form the foundations of condensed materials. The main foundational principles are emphasized, providing students with the knowledge beginners in the field should understand. The book is structured in four parts and allows students to appreciate how the concepts in this broad area build upon each other to produce a cohesive whole as they work through the chapters. Illustrations work closely with the text to convey concepts and ideas visually, enhancing student understanding of difficult material, and end-of-chapter exercises varying in difficulty allow students to put into practice the theory they have covered in each chapter and reinforce new concepts.
