Critical Points Of Two Dimensional Ising Models


Critical Points Of Two Dimensional Ising Models
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Critical Points Of Two Dimensional Ising Models


Critical Points Of Two Dimensional Ising Models
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Author : C. J. Thompson
language : en
Publisher:
Release Date : 1974

Critical Points Of Two Dimensional Ising Models written by C. J. Thompson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Ising model categories.




Conformal Invariance And Critical Phenomena


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.



The Two Dimensional Ising Model


The Two Dimensional Ising Model
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Author : Barry M. McCoy
language : en
Publisher: Courier Corporation
Release Date : 2014-03-05

The Two Dimensional Ising Model written by Barry M. McCoy and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-05 with Science categories.


Originally published in 1973, this is the definitive book on the Ising model, a mathematical model of ferromagnetism in statistical mechanics. This updated edition of the classic text features an extensive section on new developments.



Introduction To Conformal Invariance And Its Applications To Critical Phenomena


Introduction To Conformal Invariance And Its Applications To Critical Phenomena
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Author : Philippe Christe
language : en
Publisher: Springer
Release Date : 2014-08-23

Introduction To Conformal Invariance And Its Applications To Critical Phenomena written by Philippe Christe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-23 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.



Pair Correlation Effects In Many Body Systems


Pair Correlation Effects In Many Body Systems
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Author : Kristian Blom
language : en
Publisher: Springer Nature
Release Date : 2023-05-26

Pair Correlation Effects In Many Body Systems written by Kristian Blom and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-26 with Science categories.


The laws of nature encompass the small, the large, the few, and the many. In this book, we are concerned with classical (i.e., not quantum) many-body systems, which refers to any microscopic or macroscopic system that contains a large number of interacting entities. The nearest-neighbor Ising model, originally developed in 1920 by Wilhelm Lenz, forms a cornerstone in our theoretical understanding of collective effects in classical many-body systems and is to date a paradigm in statistical physics. Despite its elegant and simplistic description, exact analytical results in dimensions equal and larger than two are difficult to obtain. Therefore, much work has been done to construct methods that allow for approximate, yet accurate, analytical solutions. One of these methods is the Bethe-Guggenheim approximation, originally developed independently by Hans Bethe and Edward Guggenheim in 1935. This approximation goes beyond the well-known mean field approximation and explicitly accounts for pair correlations between the spins in the Ising model. In this book, we embark on a journey to exploit the full capacity of the Bethe-Guggenheim approximation, in non-uniform and non-equilibrium settings. Throughout we unveil the non-trivial and a priori non-intuitive effects of pair correlations in the classical nearest-neighbor Ising model, which are taken into account in the Bethe-Guggenheim approximation and neglected in the mean field approximation.



A Student S Guide To The Ising Model


A Student S Guide To The Ising Model
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Author : James S. Walker
language : en
Publisher: Cambridge University Press
Release Date : 2023-04-30

A Student S Guide To The Ising Model written by James S. Walker 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 2023-04-30 with Science categories.


A focused and accessible guide to the Ising model, a mathematical framework used to describe ferromagnetism, with exercises included.



Statistical Mechanics For Chemistry And Materials Science


Statistical Mechanics For Chemistry And Materials Science
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Author : Biman Bagchi
language : en
Publisher: CRC Press
Release Date : 2018-07-06

Statistical Mechanics For Chemistry And Materials Science written by Biman Bagchi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Science categories.


This book covers the broad subject of equilibrium statistical mechanics along with many advanced and modern topics such as nucleation, spinodal decomposition, inherent structures of liquids and liquid crystals. Unlike other books on the market, this comprehensive text not only deals with the primary fundamental ideas of statistical mechanics but also covers contemporary topics in this broad and rapidly developing area of chemistry and materials science.



Cellular Automata


Cellular Automata
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Author : Alejandro Salcido
language : en
Publisher: BoD – Books on Demand
Release Date : 2011-04-11

Cellular Automata written by Alejandro Salcido and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-11 with Computers categories.


Cellular automata make up a class of completely discrete dynamical systems, which have became a core subject in the sciences of complexity due to their conceptual simplicity, easiness of implementation for computer simulation, and their ability to exhibit a wide variety of amazingly complex behavior. The feature of simplicity behind complexity of cellular automata has attracted the researchers' attention from a wide range of divergent fields of study of science, which extend from the exact disciplines of mathematical physics up to the social ones, and beyond. Numerous complex systems containing many discrete elements with local interactions have been and are being conveniently modelled as cellular automata. In this book, the versatility of cellular automata as models for a wide diversity of complex systems is underlined through the study of a number of outstanding problems using these innovative techniques for modelling and simulation.



Statistical Mechanics And Field Theory Proceedings Of The Seventh Physics Summer School


Statistical Mechanics And Field Theory Proceedings Of The Seventh Physics Summer School
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Author : Bazhanov Vladimir V
language : en
Publisher: World Scientific
Release Date : 1995-12-21

Statistical Mechanics And Field Theory Proceedings Of The Seventh Physics Summer School written by Bazhanov Vladimir V and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-21 with categories.


This proceedings volume aims to expose graduate students to the basic ideas of field theory and statistical mechanics and to give them an understanding and appreciation of current topical research.



Cellular Automata


Cellular Automata
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Author : Peter M.A. Sloot
language : en
Publisher: Springer
Release Date : 2004-09-28

Cellular Automata written by Peter M.A. Sloot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-28 with Computers categories.


This book constitutes the refereed proceedings of the 6th International Conference on Cellular Automata for Research and Industry, ACRI 2004, held in Amsterdam, The Netherlands in October 2004. The 60 revised full papers and 30 poster papers presented were carefully reviewed and selected from 150 submissions. The papers are devoted to methods and theory; evolved cellular automata; traffic, networks, and communication; applications in science and engineering; biomedical applications, natural phenomena and ecology; and social and economical applications.