Multicritical Phenomena

Multicritical Phenomena
Author: Roger Pynn
Publisher: Springer Science & Business Media
Total Pages: 465
Release: 2012-12-06
Genre: Science
ISBN: 1461327415

This book comprises the Proceedings of a NATO Advanced Study Institute on Mu1ticritica1 Phenomena held in Geilo, Norway, between 10-21 April 1983. This school was the seventh to be held in Gei10, on various aspects of phase transitions. In spite of its apparently restrictive title the school was planned as a forum for the discus sion of phase transitions and instabilities in systems, with competing interactions and competing order parameters. Thus, in addition to the canonical multicritical points, subjects were diverse as critical phenomena in random magnetic systems and routes to chaos were discussed. The subject matter of the school is naturally divided into a series of categories which to some extent, reflect the historical development of interest in competing phenomena at phase transitions. Multicritical points in equilibrium systems, defined phenomenolo gically as points of sudden change of behaviour on an otherwise smooth phase boundary, were the first topics of the school. The theo retical consensus which has emerged during the past decade, largely as a result of calculations with the renormalisation group, was reviewed in some detail. The results presented, however, apply only to pure systems (in which dirt and other manifestations of reality are irrelevant) in that small realm close to the phase transition knoYln as "asymtopia.

Introduction to the Theory of Critical Phenomena

Introduction to the Theory of Critical Phenomena
Author: Dimo I. Uzunov
Publisher: World Scientific
Total Pages: 701
Release: 2010
Genre: Science
ISBN: 9814299480

This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.

Field Theory, The Renormalization Group, And Critical Phenomena: Graphs To Computers (3rd Edition)

Field Theory, The Renormalization Group, And Critical Phenomena: Graphs To Computers (3rd Edition)
Author: Daniel J Amit
Publisher: World Scientific Publishing Company
Total Pages: 568
Release: 2005-06-21
Genre: Science
ISBN: 9813102071

This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. Non-perturbative methods and numerical simulations are introduced in this new edition. Abundant references to research literature complement this matter-of-fact approach. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.The following new chapters are included:I. Real Space MethodsII. Finite Size ScalingIII. Monte Carlo Methods. Numerical Field Theory

Theory of Critical Phenomena in Finite-size Systems

Theory of Critical Phenomena in Finite-size Systems
Author: ?ordan Brankov
Publisher: World Scientific
Total Pages: 468
Release: 2000
Genre: Science
ISBN: 9789810239251

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.

Critical Phenomena in Liquids and Liquid Crystals

Critical Phenomena in Liquids and Liquid Crystals
Author: Mikhail Alekseevich Anisimov
Publisher: CRC Press
Total Pages: 452
Release: 1991
Genre: Critical phenomena (Physics).
ISBN: 9782881248061

Phase transitions and critical phenomena in liquids and liquid crystals have been the subject of intensive research since the 1960s. However, books on this fascinating subject have tended to be written by theorists for theorists. Professor Anisimov offers us a new approach: he aims to introduce experimentalists to the modern theories and their applications. After introducing the thermodynamics of phase transitions, he presents the modern theory of critical phenomena. He then concludes by illustrating the utility of this theory in the analysis of experimental measurements in classical fluids and binary mixtures, superfluid mixtures of helium isotopes and liquid crystals. Not only will this book be enjoyed by experimental physicists, chemists and material scientists, it will also offer the theorist an insight into the interpretation of the experimentalist's work.

Critical Phenomena in Natural Sciences

Critical Phenomena in Natural Sciences
Author: Didier Sornette
Publisher: Springer Science & Business Media
Total Pages: 445
Release: 2013-04-17
Genre: Science
ISBN: 366204174X

A modern up-to-date introduction for readers outside statistical physics. It puts emphasis on a clear understanding of concepts and methods and provides the tools that can be of immediate use in applications.

Field Theory, The Renormalization Group And Critical Phenomena (2nd Edition)

Field Theory, The Renormalization Group And Critical Phenomena (2nd Edition)
Author: Daniel J Amit
Publisher: World Scientific Publishing Company
Total Pages: 412
Release: 1984-08-31
Genre:
ISBN: 9813104147

This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.

Modern Theory Of Critical Phenomena

Modern Theory Of Critical Phenomena
Author: Shang-keng Ma
Publisher: Routledge
Total Pages: 591
Release: 2018-05-04
Genre: Social Science
ISBN: 0429967438

An important contributor to our current understanding of critical phenomena, Ma introduces the beginner--especially the graduate student with no previous knowledge of the subject-to fundamental theoretical concepts such as mean field theory, the scaling hypothesis, and the renormalization group. He then goes on to apply the renormalization group to selected problems, with emphasis on the underlying physics and the basic assumptions involved.

The Theory of Critical Phenomena

The Theory of Critical Phenomena
Author: J. J. Binney
Publisher: Oxford University Press
Total Pages: 477
Release: 1992-06-11
Genre: Science
ISBN: 0191660566

The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.

Encyclopedia of Chemical Physics and Physical Chemistry

Encyclopedia of Chemical Physics and Physical Chemistry
Author: John H. Moore
Publisher: CRC Press
Total Pages: 986
Release: 2023-07-03
Genre: Science
ISBN: 1003803288

The Encyclopedia of Physical Chemistry and Chemical Physics introduces possibly unfamiliar areas, explains important experimental and computational techniques, and describes modern endeavors. The encyclopedia quickly provides the basics, defines the scope of each subdiscipline, and indicates where to go for a more complete and detailed explanation. Particular attention has been paid to symbols and abbreviations to make this a user-friendly encyclopedia. Care has been taken to ensure that the reading level is suitable for the trained chemist or physicist. The encyclopedia is divided in three major sections: FUNDAMENTALS: the mechanics of atoms and molecules and their interactions, the macroscopic and statistical description of systems at equilibrium, and the basic ways of treating reacting systems. The contributions in this section assume a somewhat less sophisticated audience than the two subsequent sections. At least a portion of each article inevitably covers material that might also be found in a modern, undergraduate physical chemistry text. METHODS: the instrumentation and fundamental theory employed in the major spectroscopic techniques, the experimental means for characterizing materials, the instrumentation and basic theory employed in the study of chemical kinetics, and the computational techniques used to predict the static and dynamic properties of materials. APPLICATIONS: specific topics of current interest and intensive research. For the practicing physicist or chemist, this encyclopedia is the place to start when confronted with a new problem or when the techniques of an unfamiliar area might be exploited. For a graduate student in chemistry or physics, the encyclopedia gives a synopsis of the basics and an overview of the range of activities in which physical principles are applied to chemical problems. It will lead any of these groups to the salient points of a new field as rapidly as possible and gives pointers as to where to read about the topic in more detail.