Finite Size Scaling
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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.
Finite Size Scaling And Numerical Simulation Of Statistical Systems
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Author : Privman Vladimir
language : en
Publisher: World Scientific
Release Date : 1990-01-01
Finite Size Scaling And Numerical Simulation Of Statistical Systems written by Privman Vladimir and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with categories.
The theory of Finite Size Scaling describes a build-up of the bulk properties when a small system is increased in size. This description is particularly important in strongly correlated systems where critical fluctuations develop with increasing system size, including phase transition points, polymer conformations. Since numerical computer simulations are always done with finite samples, they rely on the Finite Size Scaling theory for data extrapolation and analysis. With the advent of large scale computing in recent years, the use of the size-scaling methods has become increasingly important.
Finite Size Scaling
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Author : John L. Cardy
language : en
Publisher: Elsevier Science Limited
Release Date : 1988-01-01
Finite Size Scaling written by John L. Cardy and has been published by Elsevier Science Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Science 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.
Theory Of Critical Phenomena In Finite Size Systems
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Author : ?ordan Brankov
language : en
Publisher: World Scientific
Release Date : 2000
Theory Of Critical Phenomena In Finite Size Systems written by ?ordan Brankov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.
The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals the intimate mechanism of how the critical singularities build up in the thermodynamic limit; and (4) can be fruitfully used to explain the low-temperature behaviour of quantum critical systems. The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results.
Introduction To Finite Size Scaling
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Author : Ĭordan Brankov
language : en
Publisher: Cornell University Press
Release Date : 1996
Introduction To Finite Size Scaling written by Ĭordan Brankov and has been published by Cornell University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Science categories.
Theory Of Critical Phenomena In Finite Size Systems
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Author : Jordan G Brankov
language : en
Publisher: World Scientific
Release Date : 2000-08-21
Theory Of Critical Phenomena In Finite Size Systems written by Jordan G Brankov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-21 with Science categories.
The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals the intimate mechanism of how the critical singularities build up in the thermodynamic limit; and (4) can be fruitfully used to explain the low-temperature behaviour of quantum critical systems. The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results. Contents:Overview of Critical Phenomena in Bulk SystemsThe Approximating Hamiltonian MethodExactly Solved ModelsFinite-Size Scaling at CriticalityLong-Range InteractionsModified Finite-Size ScalingBoundary EffectsFinite-Size Scaling at First Order TransitionsLimit Gibbs States and Finite-Size ScalingBulk Quantum SystemsThe Casimir EffectSurvey of Results on the Casimir Effect Readership: Graduate students and researchers in theoretical and condensed matter physics. Keywords:Phase Transition;Critical Phenomena;Finite Size Scaling;Quantum Phase TransitionsReviews: “… this book offers a careful survey of finite-size scaling near bulk phase transitions …” Journal of Statistical Physics “The book is a very comprehensive and detailed account of this field … I have found the final section on the Casimir effect particularly interesting. It is very well written and detailed … I recommend it to serious students of critical phenomena and condensed matter, but those who already have the basic knowledge of the theory of phase transitions.” Contemporary Physics
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.
Complexity And Criticality
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Author : Kim Christensen
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-10-03
Complexity And Criticality written by Kim Christensen and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-03 with Science categories.
This book provides a challenging and stimulating introduction to the contemporary topics of complexity and criticality, and explores their common basis of scale invariance, a central unifying theme of the book. Criticality refers to the behaviour of extended systems at a phase transition where scale invariance prevails. The many constituent microscopic parts bring about macroscopic phenomena that cannot be understood by considering a single part alone. The phenomenology of phase transitions is introduced by considering percolation, a simple model with a purely geometrical phase transition, thus enabling the reader to become intuitively familiar with concepts such as scale invariance and renormalisation. The Ising model is then introduced, which captures a thermodynamic phase transition from a disordered to an ordered system as the temperature is lowered in zero external field. By emphasising analogies between percolation and the Ising model, the reader's intuition of phase transitions is developed so that the underlying theoretical formalism may be appreciated fully. These equilibrium systems undergo a phase transition only if an external agent finely tunes certain external parameters to particular values. Besides fractals and phase transitions, there are many examples in Nature of the emergence of such complex behaviour in slowly driven non-equilibrium systems: earthquakes in seismic systems, avalanches in granular media and rainfall in the atmosphere. A class of non-equilibrium systems, not constrained by having to tune external parameters to obtain critical behaviour, is addressed in the framework of simple models, revealing that the repeated application of simple rules may spontaneously give rise to emergent complex behaviour not encoded in the rules themselves. The common basis of complexity and criticality is identified and applied to a range of non-equilibrium systems. Finally, the reader is invited to speculate whether self-organisation in non-equilibrium systems might be a unifying concept for disparate fields such as statistical mechanics, geophysics and atmospheric physics. Visit http://www.complexityandcriticality.com for animations for the models in the book (available for Windows and Linux), solutions to exercises, as well as a list with corrections. Contents:Percolation:Percolating Phase TransitionPercolation in One DimensionPercolation on the Bethe LatticePercolation in Two DimensionsGeometric Properties of ClustersScaling Ansatz, Scaling Functions and Scaling RelationsFinite-Size ScalingUniversalityReal-Space Renormalisation GroupIsing Model:Review of Thermodynamics and Statistical MechanicsSymmetry BreakingFerromagnetic Phase TransitionIsing Model in One DimensionMean-Field Ising ModelIsing Model in Two DimensionsLandau Theory of Continuous Phase TransitionsScaling Ansatz, Scaling Functions and Scaling RelationsUniversalityReal-Space Renormalisation GroupSelf-Organised Criticality:Non-equilibrium steady state systemBTW Model in One DimensionMean-Field Theory of the BTW ModelBranching ProcessScaling Ansatz, Scaling Functions and Scaling RelationsBTW Model in Two DimensionsA Rice Pile Experiment and the Oslo ModelEarthquakes and the OFC ModelRainfallSelf-Organised Criticality as a Unifying Principle Readership: Students at all levels, researchers and instructors looking for an introduction to the ideas of complexity and criticality.
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.
Scale Invariance
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Author : Annick LESNE
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-04
Scale Invariance written by Annick LESNE 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 2011-11-04 with Science categories.
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.