Download or read book Finite Size Scaling written by J. Cardy and published by Elsevier. This book was released on 2012-12-02 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Size Scaling And Numerical Simulation Of Statistical Systems written by Privman Vladimir and published by World Scientific. This book was released on 1990-01-01 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theory of Critical Phenomena in Finite Size Systems written by Jordan G Brankov and published by World Scientific. This book was released on 2000-08-21 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Scaling and Renormalization in Statistical Physics written by John Cardy and published by Cambridge University Press. This book was released on 1996-04-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite size Scaling written by John L. Cardy and published by Elsevier Science Limited. This book was released on 1988-01-01 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scale Invariance written by Annick LESNE and published by Springer Science & Business Media. This book was released on 2011-11-04 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Directed Models of Polymers Interfaces and Clusters Scaling and Finite Size Properties written by Vladimir Privman and published by Springer. This book was released on 1989-08-23 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a detailed introductory exposition of research results for various models, mostly two-dimensional, of directed walks, interfaces, wetting, surface adsorption (of polymers), stacks, compact clusters (lattice animals), etc. The unifying feature of these models is that in most cases they can be solved analytically. The methods used include transfer matrices, generating functions, recurrence relations, and difference equations, and in some cases involve utilization of less familiar mathematical techniques such as continued fractions and q-series. The authors emphasize an overall view of what can be learned generally of the statistical mechanics of anisotropic systems, including phenomena near surfaces, by studying the solvable models. Thus, the concept of scaling and, where known, finite-size scaling properties are elucidated. Scaling and statistical mechanics of anisoptropic systems in general are active research topics. The volume provides a comprehensive survey of exact model results in this field.
Download or read book Finite Size Effects in Correlated Electron Models written by Andrei A. Zvyagin and published by World Scientific. This book was released on 2005 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents exact results for one-dimensional models (including quantum spin models) of strongly correlated electrons in a comprehensive and concise manner. It incorporates important results related to magnetic and hybridization impurities in electron hosts and contains exact original results for disordered ensembles of impurities in interacting systems. These models describe a number of real low-dimensional electron systems that are widely used in nanophysics and microelectronics.An important method of modern theoretical and mathematical physics — the Bethe's Ansatz (BA) — is introduced to readers. This book presents different forms of the BA for periodic and open quantum chains. Other forms dealt with are the co-ordinate BA, thermodynamic BA, nested BA, algebraic BA, and thermal BA. The book also contains a compact description of other theoretical methods such as scaling, conformal field theory, Abelian and non-Abelian bosonizations.The book is suitable for use as a textbook by graduate students in non-perturbative methods of low-dimensional quantum many-body theory. It will also be a useful source of reference for qualified physicists, as well as non-experts in low-dimensional physics, as it explores material necessary for further studies in the fields of exactly solvable quantum models and low-dimensional correlated electron systems.
Download or read book The Two Dimensional Ising Model written by Barry M. McCoy and published by Courier Corporation. This book was released on 2014-03-05 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Currents Physics Sources and Commments Finite Size Scaling Vol 2 written by and published by . This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conformal Invariance and Critical Phenomena written by Malte Henkel and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 433 pages. 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.
Download or read book Theory of Critical Phenomena in Finite size Systems written by ?ordan Brankov and published by World Scientific. This book was released on 2000 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Monte Carlo Simulation in Statistical Physics written by Kurt Binder and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo Simulation in Statistical Physics deals with the computer simulation of many-body systems in condensed-matter physics and related fields of physics, chemistry and beyond, to traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, probability distributions are calculated, allowing the estimation of the thermodynamic properties of various systems. This book describes the theoretical background to several variants of these Monte Carlo methods and gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results. This fourth edition has been updated and a new chapter on Monte Carlo simulation of quantum-mechanical problems has been added. To help students in their work a special web server has been installed to host programs and discussion groups (http://wwwcp.tphys.uni-heidelberg.de). Prof. Binder was the winner of the Berni J. Alder CECAM Award for Computational Physics 2001.
Download or read book Scaling of Differential Equations written by Hans Petter Langtangen and published by Springer. This book was released on 2016-06-15 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
Download or read book Non Equilibrium Phase Transitions written by Malte Henkel and published by Springer Science & Business Media. This book was released on 2008-11-27 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.
Download or read book Equilibrium Statistical Mechanics of Lattice Models written by David A. Lavis and published by Springer. This book was released on 2015-01-31 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg--Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi--Hijmans--De Boer hierarchy of approximations. In Part III the use of algebraic, transformation and decoration methods to obtain exact system information is considered. This is followed by an account of the use of transfer matrices for the location of incipient phase transitions in one-dimensionally infinite models and for exact solutions for two-dimensionally infinite systems. The latter is applied to a general analysis of eight-vertex models yielding as special cases the two-dimensional Ising model and the six-vertex model. The treatment of exact results ends with a discussion of dimer models. In Part IV series methods and real-space renormalization group transformations are discussed. The use of the De Neef—Enting finite-lattice method is described in detail and applied to the derivation of series for a number of model systems, in particular for the Potts model. The use of Pad\'e, differential and algebraic approximants to locate and analyze second- and first-order transitions is described. The realization of the ideas of scaling theory by the renormalization group is presented together with treatments of various approximation schemes including phenomenological renormalization. Part V of the book contains a collection of mathematical appendices intended to minimise the need to refer to other mathematical sources.
Download or read book The Casimir Effect in Critical Systems written by Michael Krech and published by World Scientific. This book was released on 1994 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The well-known Casimir effect has a direct analogue in systems near critical or multicritical points. Critical fluctuations in systems confined to finite geometries lead to attractive or repulsive forces between system boundaries. These forces influence the formation of wetting layers of liquid 4He or binary liquid mixtures near critical points in these fluids. With the aid of recently developed versions of the atomic force microscope, these forces appear to be directly measurable. The book contains an introduction to the physics of critical phenomena and reviews the most recent developments in the theory of finite-size scaling. A detailed discussion of the Casimir effect and related questions follows. The analysis of quantitative effects on the specific heat of critical films, the formation of wetting layers, and force measurements finish the presentation. This is perhaps the first book on the critical Casimir effect.
