Scaling and Renormalization in Statistical Physics


Author: John Cardy
Publisher: Cambridge University Press
ISBN: 9780521499590
Category: Science
Page: 238
View: 4258

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A thoroughly modern graduate-level introduction to the theory of critical behaviour. Covers phase transitions, mean field theory, phase diagrams, fixed points, cross-over behaviour, finite-size scaling, a simple approach to the epsilon expansion, low-dimensional systems, surface critical behaviour, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. Includes many problems.

Statistical Physics of Fields


Author: Mehran Kardar
Publisher: Cambridge University Press
ISBN: 1139855883
Category: Science
Page: N.A
View: 8263

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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.

Lectures On Phase Transitions And The Renormalization Group


Author: Nigel Goldenfeld
Publisher: CRC Press
ISBN: 0429973128
Category: Science
Page: 420
View: 7908

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Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.

Statistical Mechanics of Phase Transitions


Author: J. M. Yeomans
Publisher: Clarendon Press
ISBN: 0191589705
Category:
Page: 164
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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. -

Non-equilibrium Statistical Mechanics and Turbulence


Author: John Cardy,Gregory Falkovich,Krzysztof Gawedzki
Publisher: Cambridge University Press
ISBN: 9780521715140
Category: Mathematics
Page: 161
View: 8360

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This self-contained volume introduces modern methods of statistical mechanics in turbulence, with three harmonised lecture courses by world class experts.

Statistical Physics of Particles


Author: Mehran Kardar
Publisher: Cambridge University Press
ISBN: 1139464876
Category: Science
Page: N.A
View: 3146

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Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.

Local Quantum Physics

Fields, Particles, Algebras
Author: Rudolf Haag
Publisher: Springer Science & Business Media
ISBN: 3642614582
Category: Science
Page: 392
View: 2707

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The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems appear in a different light. It includes a section on the assumptions leading to the specific mathematical formalism of quantum theory and a section entitled "The evolutionary picture" describing my personal conclusions. Alto gether the discussion suggests that the conventional language is too narrow and that neither the mathematical nor the conceptual structure are built for eter nity. Future theories will demand radical changes though not in the direction of a return to determinism. Essential lessons taught by Bohr will persist. This chapter is essentially self-contained. Some new material has been added in the last chapter. It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds. A few pages on renor malization have been added in Chapter II and some effort has been invested in the search for mistakes and unclear passages in the first edition. The central objective of the book, expressed in the title "Local Quantum Physics", is the synthesis between special relativity and quantum theory to gether with a few other principles of general nature.

Principles of Condensed Matter Physics


Author: P. M. Chaikin,T. C. Lubensky
Publisher: Cambridge University Press
ISBN: 1139643053
Category: Science
Page: N.A
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Now in paperback, this book provides an overview of the physics of condensed matter systems. Assuming a familiarity with the basics of quantum mechanics and statistical mechanics, the book establishes a general framework for describing condensed phases of matter, based on symmetries and conservation laws. It explores the role of spatial dimensionality and microscopic interactions in determining the nature of phase transitions, as well as discussing the structure and properties of materials with different symmetries. Particular attention is given to critical phenomena and renormalization group methods. The properties of liquids, liquid crystals, quasicrystals, crystalline solids, magnetically ordered systems and amorphous solids are investigated in terms of their symmetry, generalised rigidity, hydrodynamics and topological defect structure. In addition to serving as a course text, this book is an essential reference for students and researchers in physics, applied physics, chemistry, materials science and engineering, who are interested in modern condensed matter physics.

Finite-Size Scaling


Author: J. Cardy
Publisher: Elsevier
ISBN: 0444596062
Category: Science
Page: 384
View: 8202

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Over the past few years, finite-size scaling has become an increasingly important tool in studies of critical systems. This is partly due to an increased understanding of finite-size effects by analytical means, and partly due to our ability to treat larger systems with large computers. The aim of this volume was to collect those papers which have been important for this progress and which illustrate novel applications of the method. The emphasis has been placed on relatively recent developments, including the use of the &egr;-expansion and of conformal methods.

Quantum Field Theory of Many-Body Systems

From the Origin of Sound to an Origin of Light and Electrons
Author: Xiao-Gang Wen
Publisher: Oxford University Press on Demand
ISBN: 0198530943
Category: Science
Page: 505
View: 7591

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This book is a pedagogical and systematic introduction to new concepts and quantum field theoretical methods in condensed matter physics, which may have an impact on our understanding of the origin of light, electrons and other elementary particles in the universe. Emphasis is on clear physical principles, while at the same time bringing students to the fore of today's research.

Quantum Field Theory in Condensed Matter Physics


Author: Naoto Nagaosa
Publisher: Springer Science & Business Media
ISBN: 3662037742
Category: Science
Page: 206
View: 7340

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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.

Scaling Concepts in Polymer Physics


Author: Pierre-Gilles de Gennes
Publisher: Cornell University Press
ISBN: 9780801412035
Category: Science
Page: 324
View: 9900

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The first stage of the physics of long, flexible chains was pioneered by eminent scientists such as Debye, Kuhn, Kramers, and Flory, who formulated the basic ideas. In recent years, because of the availability of new experimental and theoretical tools, a second stage of the physics of polymers has evolved. In this book, a noted physicist explains the radical changes that have taken place in this exciting and rapidly developing field.Pierre-Gilles de Gennes points out the three developments that have been essential for recent advances in the study of large-scale conformations and motions of flexible polymers in solutions and melts. They are the advent of neutron-scattering experiments on selectively deuterated molecules; the availability of inelastic scattering of laser light, which allows us to study the cooperative motions of the chains; and the discovery of an important relationship between polymer statistics and critical phenomena, leading to many simple scaling laws.Until now, information relating to these advances has not been readily accessible to physical chemists and polymer scientists because of the difficulties in the new theoretical language that has come into use. Professor de Gennes bridges this gap by presenting scaling concepts in terms that will be understandable to students in chemistry and engineering as well as in physics.

Condensed Matter Field Theory


Author: Alexander Altland,Ben D. Simons
Publisher: Cambridge University Press
ISBN: 113948513X
Category: Science
Page: N.A
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Modern experimental developments in condensed matter and ultracold atom physics present formidable challenges to theorists. This book provides a pedagogical introduction to quantum field theory in many-particle physics, emphasizing the applicability of the formalism to concrete problems. This second edition contains two new chapters developing path integral approaches to classical and quantum nonequilibrium phenomena. Other chapters cover a range of topics, from the introduction of many-body techniques and functional integration, to renormalization group methods, the theory of response functions, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion focuses on practical experimental applications drawn largely from condensed matter physics and neighboring fields. Extended and challenging problems with fully worked solutions provide a bridge between formal manipulations and research-oriented thinking. Aimed at elevating graduate students to a level where they can engage in independent research, this book complements graduate level courses on many-particle theory.

The Universe in a Helium Droplet


Author: G. E. Volovik
Publisher: Oxford University Press on Demand
ISBN: 0198507828
Category: Foreign Language Study
Page: 509
View: 3417

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There are fundamental relations between three vast areas of physics: particle physics, cosmology and condensed matter physics. The fundamental links between the first two areas, in other words, between micro- and macro-worlds, have been well established. There is a unified system of laws governing the scales from subatomic particles to the Cosmos and this principle is widely exploited in the description of the physics of the early Universe. The main goal of this book is to establish and define the connection of these two fields with condensed matter physics. According to the modern view, elementary particles (electrons, neutrinos, quarks, etc.) are excitations of a more fundamental medium called the quantum vacuum. This is the new 'aether' of the 21st Century. Electromagnetism, gravity, and the fields transferring weak and strong interactions all represent different types of the collective motion of the quantum vacuum. Among the existing condensed matter systems, a quantum liquid called superfluid 3He-A most closely represents the quantum vacuum. Its quasiparticles are very similar to the elementary particles, while the collective modes of the liquid are very similar to electromagnetic and gravitational fields, and the quanta of these collective modes are analogues of photons and gravitons. The fundamental laws of physics, such as the laws of relativity (Lorentz invariance) and gauge invariance, arise when the temperature of the quantum liquid decreases. This book is written for graduate students and researchers in all areas of physics.

Statistical Field Theory


Author: Giorgio Parisi
Publisher: Westview Press
ISBN: 9780738200514
Category: Science
Page: 366
View: 4905

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Specifically written to introduce researchers and advanced students to the modern developments in statistical mechanics and field theory, this book's leitmotiv is functional integration and its application to different areas of physics. The book acts as both an introduction to and a lucid overview of the major problems in statistical field theory.

Nonequilibrium Statistical Physics

A Modern Perspective
Author: Roberto Livi,Paolo Politi
Publisher: Cambridge University Press
ISBN: 1108364047
Category: Science
Page: N.A
View: 4300

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Statistical mechanics has been proven to be successful at describing physical systems at thermodynamic equilibrium. Since most natural phenomena occur in nonequilibrium conditions, the present challenge is to find suitable physical approaches for such conditions: this book provides a pedagogical pathway that explores various perspectives. The use of clear language, and explanatory figures and diagrams to describe models, simulations and experimental findings makes the book a valuable resource for undergraduate and graduate students, and also for lecturers organizing teaching at varying levels of experience in the field. Written in three parts, it covers basic and traditional concepts of nonequilibrium physics, modern aspects concerning nonequilibrium phase transitions, and application-orientated topics from a modern perspective. A broad range of topics is covered, including Langevin equations, Levy processes, directed percolation, kinetic roughening and pattern formation.

Elements of Phase Transitions and Critical Phenomena


Author: Hidetoshi Nishimori,Gerardo Ortiz
Publisher: Oxford University Press
ISBN: 0199577226
Category: Science
Page: 358
View: 3369

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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.