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Conformal Invariance And Critical Phenomena

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Conformal Invariance And Critical Phenomena

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Author : Malte Henkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Conformal Invariance And Critical Phenomena written by Malte Henkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.

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.

Introduction To Conformal Invariance And Its Applications To Critical Phenomena

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Author : Philippe Christe
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-11

Introduction To Conformal Invariance And Its Applications To Critical Phenomena written by Philippe Christe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-11 with Science categories.

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.

Conformal Invariance And Critical Phenomena

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Author : Malte Henkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-04-16

This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators. Numerical methods for matrix diagonalization are described as well as finite-size scaling techniques and their conformal extensions. Many exercises are included. Applications treat the Ising, Potts, chiral Potts, Yang-Lee, percolation and XY models, the XXZ chain, linear polymers, tricritical points, conformal turbulence, surface criticality and profiles, defect lines and aperiodically modulated systems, persistent currents and dynamical scaling. The vicinity of the critical point is studied culminating in the exact solution of the two-dimensional Ising model at the critical temperature in a magnetic field. Relevant experimental results are also reviewed.

Conformal Invariance And Applications To Statistical Mechanics

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Author : Claude Itzykson
language : en
Publisher: World Scientific
Release Date : 1988

Conformal Invariance And Applications To Statistical Mechanics written by Claude Itzykson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Science categories.

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.

Conformal Invariance And Applications To Statistical Mechanics

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Author : C Itzykson
language : en
Publisher: World Scientific
Release Date : 1998-09-29

Conformal Invariance And Applications To Statistical Mechanics written by C Itzykson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-29 with categories.

Scaling And Renormalization In Statistical Physics

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Author : John Cardy
language : en
Publisher: Cambridge University Press
Release Date : 1996-04-26

Scaling And Renormalization In Statistical Physics written by John Cardy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-04-26 with Science categories.

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.

Elements Of Phase Transitions And Critical Phenomena

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Author : Hidetoshi Nishimori
language : en
Publisher: Oxford University Press
Release Date : 2011

Elements Of Phase Transitions And Critical Phenomena written by Hidetoshi Nishimori and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.

Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.

Quantum Critical Phenomena And Conformal Invariance

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Author : Zhe Chang
language : en
Publisher:
Release Date : 1995

Quantum Critical Phenomena And Conformal Invariance written by Zhe Chang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Conformal invariants categories.

Finite Size Scaling

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Author : J. Cardy
language : en
Publisher: Elsevier
Release Date : 2012-12-02

Finite Size Scaling written by J. Cardy and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Computers categories.

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.

Phase Transitions And Critical Phenomena

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Author : Cyril Domb
language : en
Publisher:
Release Date : 1991

Phase Transitions And Critical Phenomena written by Cyril Domb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Critical phenomena (Physics) categories.

Conformal Invariance And Critical Phenomena

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