Introduction To Conformal Invariance And Its Applications To Critical Phenomena

Author : Malte Henkel
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 42,9 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662039373

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Conformal Invariance and Critical Phenomena by Malte Henkel Pdf

Critical phenomena arise in a wide variety of physical systems. Classi cal examples are the liquid-vapour critical point or the paramagnetic ferromagnetic transition. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and fully developed tur bulence and may even extend to the quark-gluon plasma and the early uni verse as a whole. Early theoretical investigators tried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations, culminating in Landau's general theory of critical phenomena. Nowadays, it is understood that the common ground for all these phenomena lies in the presence of strong fluctuations of infinitely many coupled variables. This was made explicit first through the exact solution of the two-dimensional Ising model by Onsager. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is emphasized today. This can be briefly summarized by saying that at a critical point a system is scale invariant. In addition, conformal invaTiance permits also a non-uniform, local rescal ing, provided only that angles remain unchanged.

Author : Philippe Christe,Malte Henkel
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 51,7 Mb
Release : 2008-09-11
Category : Science
ISBN : 9783540475750

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Introduction to Conformal Invariance and Its Applications to Critical Phenomena by Philippe Christe,Malte Henkel Pdf

The history of critical phenomena goes back to the year 1869 when Andrews discovered the critical point of carbon dioxide, located at about 31°C and 73 atmospheres pressure. In the neighborhood ofthis point the carbon dioxide was observed to become opalescent, that is, light is strongly scattered. This is nowadays interpreted as comingfrom the strong fluctuations of the system close to the critical point. Subsequently, a wide varietyofphysicalsystems were realized to display critical points as well. Ofparticular importance was the observation of a critical point in ferromagnetic iron by Curie. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and may even extend to the quark-gluon plasmaand the early universe as a whole. Early theoretical investigationstried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations and culminating in Landau's general theory of critical phenomena. In a dramatic development, Onsager's exact solutionofthe two-dimensional Ising model made clear the important role of the critical fluctuations. Their role was taken into account in the subsequent developments leading to the scaling theories of critical phenomena and the renormalization group. These developements have achieved a precise description of the close neighborhood of the critical point and results are often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is today emphasized.

Author : Philippe Christe
Publisher : Unknown
Page : 260 pages
File Size : 52,8 Mb
Release : 1993
Category : Conformal invariants
ISBN : OCLC:1319329760

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Introduction to Conformal Invariance and Its Applications to Critical Phenomena by Philippe Christe Pdf

Author : Malte Henkel,Dragi Karevski
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 54,5 Mb
Release : 2012-04-05
Category : Science
ISBN : 9783642279348

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Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution by Malte Henkel,Dragi Karevski Pdf

Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.

Author : C Itzykson,H Saleur,Jean-bernard Zuber
Publisher : World Scientific
Page : 992 pages
File Size : 53,5 Mb
Release : 1998-09-29
Category : Electronic
ISBN : 9789814507592

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Conformal Invariance And Applications To Statistical Mechanics by C Itzykson,H Saleur,Jean-bernard Zuber Pdf

This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions.

Author : Anonim
Publisher : Springer
Page : 208 pages
File Size : 40,9 Mb
Release : 2012-04-06
Category : Electronic
ISBN : 364227935X

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Conformal Invariance by Anonim Pdf

Author : Philippe Francesco,Pierre Mathieu,David Senechal
Publisher : Springer Science & Business Media
Page : 908 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461222569

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Conformal Field Theory by Philippe Francesco,Pierre Mathieu,David Senechal Pdf

Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.

Author : John Cardy
Publisher : Cambridge University Press
Page : 264 pages
File Size : 51,5 Mb
Release : 1996-04-26
Category : Science
ISBN : 0521499593

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Scaling and Renormalization in Statistical Physics by John Cardy Pdf

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.

Author : Ferenc N. Balogh
Publisher : Nova Publishers
Page : 246 pages
File Size : 44,7 Mb
Release : 2008
Category : Business & Economics
ISBN : 1604560754

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String Theory Research Progress by Ferenc N. Balogh Pdf

String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the standard model of particle physics. The phrase is often used as shorthand for Superstring theory, as well as related theories such as M-theory. By replacing the point-like particles with strings, an apparently consistent quantum theory of gravity emerges. Moreover, it may be possible to 'unify' the known natural forces (gravitational, electromagnetic, weak nuclear and strong nuclear) by describing them with the same set of equations. Studies of string theory have revealed that it predicts higher-dimensional objects called branes. String theory strongly suggests the existence of ten or eleven (in M-theory) space-time dimensions, as opposed to the usual four (three spatial and one temporal) used in relativity theory.

Author : Uwe Grimm,Michael Baake
Publisher : World Scientific
Page : 308 pages
File Size : 42,7 Mb
Release : 1995-01-23
Category : Science
ISBN : 9789814501040

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Perspectives on Solvable Models by Uwe Grimm,Michael Baake Pdf

This volume consists of a collection of recent research articles dedicated to Vladimir Rittenberg on the occasion of his 60th birthday. Various aspects of solvable models in different areas of theoretical and mathematical physics are covered. Particular topics include diffusion, self-organized criticality, classical and quantum spin chains, two-dimensional lattice models, quantum algebras, and conformal field theory. The list of contributing authors contains altogether 34 names, including among others, Baxter, Cardy, Itzykson, Martin, McCoy, Nahm, Pearce and de Vega. Contents:PrefaceExact Steady States of Asymmetric Diffusion and Two-Species Annihilation with Back Reaction from the Ground State of Quantum Spin Models (F C Alcaraz)Schrödinger Invariance in Discrete Stochastic Systems (M Henkel & G Schütz)Exact Thermostatic Results for the n-Vector Model on the Harmonic Chain (G Junker & H Leschke)Non-Hermitian Tricriticality in the Blume-Capel Model with Imaginary Field (G von Gehlen)Fusion of A–D–E Lattice Models (Y-K Zhou & P A Pearce)A Critical Ising Model on the Labyrinth (M Baake et al.)Quantum Superspin Chains (T H Baker & P D Jarvis)q-Deformations of Quantum Spin Chains with Exact Valence-Bond Ground States (M T Batchelor & C M Yung)The Tensor Product of Tensor Operators Over Quantum Algebras: Some Applications to Quantum Spin Chains (M Scheunert)Infinite Families of Gauge-Equivalent R-Matrices and Gradations of Quantized Affine Algebras (A J Bracken et al.)Sigma Models with (2,2) World Sheet Supersymmetry (F Delduc & E Sokatchev)and other papers Readership: Theoretical physicists. keywords:

Author : Z. Horv th,L. Palla
Publisher : World Scientific
Page : 474 pages
File Size : 47,5 Mb
Release : 2001
Category : Science
ISBN : 9812799966

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Nonperturbative Quantum-field-theoretic Methods and Their Applications by Z. Horv th,L. Palla Pdf

Contents: Conformal Boundary Conditions OCo and What They Teach Us (V B Petkova & J-B Zuber); A Physical Basis for the Entropy of the AdS 3 Black Hole (S Fernando & F Mansouri); Spinon Formulation of the Kondo Problem (A Klmper & J R Reyes-Martinez); Boundary Integrable Quantum Field Theories (P Dorey); Finite Size Effects in Integrable Quantum Field Theories (F Ravanini); Nonperturbative Analysis of the Two-Frequency Sine-Gordon Model (Z Bajnok et al.); Screening in Hot SU(2) Gauge Theory and Propagators in 3D Adjoint Higgs Model (A Cucchieri et al.); Effective Average Action in Statistical Physics and Quantum Field Theory (Ch Wetterich); Phase Transitions in Non-Hermitean Matrix Models and the OC Single RingOCO Theorem (J Feinberg et al.); Unraveling the Mystery of Flavor (A Falk); The Nahm Transformation on R 2 X T 2 (C Ford); A 2D Integrable Axion Model and Target Space Duality (P Forgics); Supersymmetric Ward Identities and Chiral Symmetry Breaking in SUSY QED (M L Walker); and other papers. Readership: Theoretical, mathematical and high energy physicists."

Author : Zalan Horvath,Laszlo Palla
Publisher : World Scientific
Page : 471 pages
File Size : 47,7 Mb
Release : 2001-05-18
Category : Science
ISBN : 9789814490832

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Non-perturbative Qft Methods And Their Applications, Procs Of The Johns Hopkins Workshop On Current Problems In Particle Theory 24 by Zalan Horvath,Laszlo Palla Pdf

Contents:Conformal Boundary Conditions — and What They Teach Us (V B Petkova & J-B Zuber)A Physical Basis for the Entropy of the AdS3 Black Hole (S Fernando & F Mansouri)Spinon Formulation of the Kondo Problem (A Klümper & J R Reyes-Martinez)Boundary Integrable Quantum Field Theories (P Dorey)Finite Size Effects in Integrable Quantum Field Theories (F Ravanini)Nonperturbative Analysis of the Two-Frequency Sine-Gordon Model (Z Bajnok et al.)Screening in Hot SU(2) Gauge Theory and Propagators in 3D Adjoint Higgs Model (A Cucchieri et al.)Effective Average Action in Statistical Physics and Quantum Field Theory (Ch Wetterich)Phase Transitions in Non-Hermitean Matrix Models and the “Single Ring” Theorem (J Feinberg et al.)Unraveling the Mystery of Flavor (A Falk)The Nahm Transformation on R2 X T2 (C Ford)A 2D Integrable Axion Model and Target Space Duality (P Forgács)Supersymmetric Ward Identities and Chiral Symmetry Breaking in SUSY QED (M L Walker)and other papers Readership: Theoretical, mathematical and high energy physicists. Keywords:

Author : Eisenriegler Erich
Publisher : World Scientific
Page : 424 pages
File Size : 49,5 Mb
Release : 1993-09-30
Category : Science
ISBN : 9789813104464

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Polymers Near Surfaces: Conformation Properties And Relation To Critical Phenomena by Eisenriegler Erich Pdf

This book gives an introduction to the conformation properties near surfaces of long flexible polymer chains in extreme dilution. These properties are of both practical and fundamental importance. While the behavior in this fluctuation-dominated situation is independent of most microscopic details, it shows a large variety that is characterized by the different qualitative conditions in the bulk (good or theta solvent, etc) and near the surface (desorbing or adsorbing, etc). The main focus of the book is on powerful, recent theoretical developments that have -despite the long history of the field — increased our understanding considerably during the last few years. The close relationship to surface critical phenomena is explained, making it possible to apply advanced methods of field theory. A self-contained introduction in these approaches, and their application to polymer physics, are given assuming only a basic knowledge of statistical mechanics. A detailed consideration of ideal (random walk-type) chains near surfaces serves as a first orientation. Much of the materials have not appeared previously in book form. This text is the first to give an introduction simultaneously to the renormalization group, short distance expansions and conformal invariance in critical systems with a surface. This book will be of interest to physicists and chemists active in the field of polymers and to theoretical physicists working in statistical mechanics, critical phenomena and field theory. Due to its introductory character it will also be useful to students who intend to specialize in one of these fields, and it could also be used as a textbook for a course at senior undergraduate or graduate level.

Author : Malte Henkel,Dragi Karevski
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 44,7 Mb
Release : 2012-04-04
Category : Language Arts & Disciplines
ISBN : 9783642279331

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Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution by Malte Henkel,Dragi Karevski Pdf

Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.

Author : Yurij Holovatch
Publisher : World Scientific
Page : 264 pages
File Size : 44,5 Mb
Release : 2022-12-06
Category : Science
ISBN : 9789811260445

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Order, Disorder And Criticality: Advanced Problems Of Phase Transition Theory - Volume 7 by Yurij Holovatch Pdf

This book is the seventh volume of review chapters on advanced problems of phase transitions and critical phenomena, the former six volumes appeared in 2004, 2007, 2012, 2015, 2018, and 2020. The aim of the book is to provide reviews in those aspects of criticality and related subjects that are currently attracting much attention due to essential new contributions.The book consists of five chapters. They discuss criticality of complex systems, where the new, emergent properties appear via collective behaviour of simple elements as well as historical aspects of studies in the field of critical phenomena. Since all complex systems involve cooperative behaviour between many interconnected components, the field of phase transitions and critical phenomena provides a very natural conceptual and methodological framework for their study.As the first six volumes, this book is based on the review lectures that were given in Lviv (Ukraine) at the 'Ising lectures' — a traditional annual workshop on complex systems, phase transitions and critical phenomena which aims to bring together experts in these fields with university students and those who are interested in the subject.