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Introduction to Conformal Invariance and Its Applications to Critical Phenomena

2008-09-11 Science
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Release : 2008-09-11
Genre : Science
Kind : eBook
Book Rating : 753/5 ( reviews)

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Book Synopsis Introduction to Conformal Invariance and Its Applications to Critical Phenomena by : Philippe Christe

Download or read book Introduction to Conformal Invariance and Its Applications to Critical Phenomena written by Philippe Christe. This book was released on 2008-09-11. Available in PDF, EPUB and Kindle. Book excerpt: 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

2013-03-14 Science
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Release : 2013-03-14
Genre : Science
Kind : eBook
Book Rating : 370/5 ( reviews)

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Book Synopsis Conformal Invariance and Critical Phenomena by : Malte Henkel

Download or read book Conformal Invariance and Critical Phenomena written by Malte Henkel. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: 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

1993 Conformal invariants
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Release : 1993
Genre : Conformal invariants
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Introduction to Conformal Invariance and Its Applications to Critical Phenomena by : Philippe Christe

Download or read book Introduction to Conformal Invariance and Its Applications to Critical Phenomena written by Philippe Christe. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution

2012-04-05 Science
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Release : 2012-04-05
Genre : Science
Kind : eBook
Book Rating : 341/5 ( reviews)

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Book Synopsis Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution by : Malte Henkel

Download or read book Conformal Invariance: an Introduction to Loops, Interfaces and Stochastic Loewner Evolution written by Malte Henkel. This book was released on 2012-04-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Polymers Near Surfaces: Conformation Properties And Relation To Critical Phenomena

1993-09-30 Science
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Release : 1993-09-30
Genre : Science
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Book Rating : 465/5 ( reviews)

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

Download or read book Polymers Near Surfaces: Conformation Properties And Relation To Critical Phenomena written by Eisenriegler Erich. This book was released on 1993-09-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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