Disorder and Competition in Soluble Lattice Models
Disorder and Competition in Soluble Lattice Models

Author: Walter F. Wreszinski

Publisher: World Scientific

Published: 1993

Total Pages: 250

ISBN-13: 9789810214166

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At present, existing literature on this subject matter can only be said to relate in minor areas to this work. Important concepts in statistical mechanics, such as frustration, localization, Lifshitz and Griffiths singularities, multicritical points, modulated phases, superselection sectors, spontaneous symmetry breaking and the Haldane phase, strange attractors and the Hausdorff dimension, and many others, are illustrated by exactly soluble lattice models. There are examples of simple lattice models which are shown to give rise to spectacular phase diagrams, with multicritical points and sequences of modulated phases. The models are chosen to enable a concise exposition as well as a connection with real physical systems (as dilute antiferromagnets, spin glasses and modulated magnets). A brief introduction to the properties of dynamical systems, an overview of conformal invariance and the Bethe Ansatz and a discussion of some general methods of statistical mechanics related to spontaneous symmetry breaking, are included in the appendices. A number of exercises are included in the text to help the comprehension of the most representative issues.

Exactly Soluble Models In Statistical Mechanics - Historical Perspectives And Current Status
Exactly Soluble Models In Statistical Mechanics - Historical Perspectives And Current Status

Author: Christopher King

Publisher: World Scientific

Published: 1997-02-26

Total Pages: 234

ISBN-13: 9814546593

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This volume contains the proceedings of the conference on 'Exactly Soluble Models in Statistical Mechanics: Historical Perspectives and Current Status', held at Northeastern University in March 1996 — the first ever conference to deal exclusively with this topic. Besides invited presentations by leading researchers in the field, the conference held a session of contributed papers by participants from throughout the world. The proceedings, which include both the invited and the contributed papers, reflect the broad range of interest in exactly soluble models as well as the diverse fields in physics and mathematics that they connect. Apart from providing concise and timely reviews, the papers in this volume give a snapshot of the current state of affairs. The topics covered range from a historical survey of the field (by E H Lieb) to the latest formulation of a star-star transformation of spin models (by R J Baxter).

Lattice Statistics and Mathematical Physics
Lattice Statistics and Mathematical Physics

Author: Jacques H. H. Perk

Publisher: World Scientific

Published: 2002

Total Pages: 330

ISBN-13: 9812382038

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"Papers presented at the Nankai Symposium on 'Lattice Statistics and Mathematical Physics ... took place at the Nankai Institute of Mathematics in Tianjin, China"--P. v.

Lattice Statistics And Mathematical Physics: Festschrift Dedicated To Professor Fa-yueh Wu On The Occasion Of His 70th Birthday, Proceedings Of Apctp-nankai Joint Symposium
Lattice Statistics And Mathematical Physics: Festschrift Dedicated To Professor Fa-yueh Wu On The Occasion Of His 70th Birthday, Proceedings Of Apctp-nankai Joint Symposium

Author: Mo-lin Ge

Publisher: World Scientific

Published: 2002-11-06

Total Pages: 330

ISBN-13: 981448718X

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This book contains thirty-six short papers on recent progress in a variety of subjects in mathematical and theoretical physics, written for the proceedings of a symposium in honor of the seventieth birthday of Professor F Y Wu, held at the Nankai Institute of Mathematics, October 7-11, 2001. The collection of papers is aimed at researchers, including graduate students, with an interdisciplinary interest and gives a brief introduction to many of the topics of current interest. These include new results on exactly solvable models in statistical mechanics, integrable through the Yang-Baxter equations, quantum groups, fractional statistics, random matrices, index theorems on the lattice, combinatorics, and other related topics.

Chaos
Chaos

Author: Angelo Vulpiani

Publisher: World Scientific

Published: 2010

Total Pages: 482

ISBN-13: 9814277665

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Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.

Statistical Mechanics Of Magnetic Excitations: From Spin Waves To Stripes And Checkerboards
Statistical Mechanics Of Magnetic Excitations: From Spin Waves To Stripes And Checkerboards

Author: Enrico Rastelli

Publisher: World Scientific

Published: 2013-01-11

Total Pages: 359

ISBN-13: 9814489174

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The aim of this advanced textbook is to provide the reader with a comprehensive explanation of the ground state configurations, the spin wave excitations and the equilibrium properties of spin lattices described by the Ising-Heisenberg Hamiltonians in the presence of short (exchange) and long range (dipole) interactions.The arguments are presented in such detail so as to enable advanced undergraduate and graduate students to cross the threshold of active research in magnetism by using both analytic calculations and Monte Carlo simulations.Recent results about unorthodox spin configurations such as stripes and checkerboards should then excite theoreticians in the field of magnetism and magnetic materials research.

Introduction To Stochastic Processes And Nonequilibrium Statistical Physics, An (Revised Edition)
Introduction To Stochastic Processes And Nonequilibrium Statistical Physics, An (Revised Edition)

Author: Horacio Sergio Wio

Publisher: World Scientific Publishing Company

Published: 2012-09-05

Total Pages: 319

ISBN-13: 9814434639

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This book aims to provide a compact and unified introduction to the most important aspects in the physics of non-equilibrium systems. It first introduces stochastic processes and some modern tools and concepts that have proved their usefulness to deal with non-equilibrium systems from a purely probabilistic angle. The aim is to show the important role played by fluctuations in far-from-equilibrium situations, where noise can promote order and organization, switching among non-equilibrium states, etc. The second part adopts a more historical perspective, retracing the first steps taken from the purely thermodynamic as well as from the kinetic points of view to depart (albeit slightly) from equilibrium. The third part revisits the path outlined in the first one, but now undertakes the mesoscopic description of extended systems, where new phenomena (patterns, long-range correlations, scaling far from equilibrium, etc.) are observed.This book is a revised and extended version of an earlier edition published in 1994. It includes topics of current research interest in far-from-equilibrium situations like noise-induced phenomena and free energy-like functionals, surface growth and roughening, etc. It can be used as an advanced textbook by graduate students in physics. It also covers topics of current interest in other disciplines and interdisciplinary approaches in engineering, biophysics, and economics, among others. The level of detail in the book is enough to capture the interest of the reader and facilitate the path to more learning by exploring the modern research literature provided. At the same time, the book is also complete enough to be self-contained for those readers who just need an overview of the subject.

Non-equilibrium Thermodynamics Of Heterogeneous Systems (Second Edition)
Non-equilibrium Thermodynamics Of Heterogeneous Systems (Second Edition)

Author: Signe Kjelstrup

Publisher: World Scientific

Published: 2020-08-27

Total Pages: 492

ISBN-13: 9811216789

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This book utilizes non-equilibrium thermodynamics to describe transport in complex, heterogeneous media. There are large coupling effects between transport of heat, mass, charge and chemical reactions at surfaces, and it is important to know how one should properly integrate across systems where different phases are in contact. There is no other book available today that gives a prescription of how to set up flux equations for transports across heterogeneous systems.

Non-equilibrium Thermodynamics of Heterogeneous Systems
Non-equilibrium Thermodynamics of Heterogeneous Systems

Author: Signe Kjelstrup

Publisher: World Scientific

Published: 2008

Total Pages: 451

ISBN-13: 9812779140

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The purpose of this book is to encourage the use of non-equilibrium thermodynamics to describe transport in complex, heterogeneous media. With large coupling effects between the transport of heat, mass, charge and chemical reactions at surfaces, it is important to know how one should properly integrate across systems where different phases are in contact. No other book gives a prescription of how to set up flux equations for transports across heterogeneous systems. The authors apply the thermodynamic description in terms of excess densities, developed by Gibbs for equilibrium, to non-equilibrium systems. The treatment is restricted to transport into and through the surface. Using local equilibrium together with the balance equations for the surface, expressions for the excess entropy production of the surface and of the contact line are derived. Many examples are given to illustrate how the theory can be applied to coupled transport of mass, heat, charge and chemical reactions; in phase transitions, at electrode surfaces and in fuel cells. Molecular simulations and analytical studies are used to add insight. Sample Chapter(s). Chapter 1: Scope (169 KB). Contents: General Theory: The Entropy Production for a Homogeneous Phase: The Excess Entropy Production for the Surface; Flux Equations and Onsager Relations; Transport of Heat and Mass; Transport of Mass and Charge; Applications: Evaporation and Condensation; A Nonisothermal Concentration Cell; Adiabatic Electrode Reactions; The Formation Cell; Modeling the Polymer Electrolyte Fuel Cell; The Impedance of an Electrode Surface; The Non-Equilibrium Two-Phase van der Waals Model; and other chapters. Readership: Graduate students, researchers, lecturers and professionals in physics, nanoscience and surface science.

Statistical Physics On The Eve Of The 21st Century: In Honour Of J B Mcguire On The Occasion Of His 65th Birthday
Statistical Physics On The Eve Of The 21st Century: In Honour Of J B Mcguire On The Occasion Of His 65th Birthday

Author: Luc T Wille

Publisher: World Scientific

Published: 1999-02-04

Total Pages: 536

ISBN-13: 9814544167

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This volume is a collection of original papers and reviews in honour of James McGuire, one of the pioneers of integrable models in statistical physics. The broad range of articles offers a timely perspective on the current status of statistical mechanics, identifying both recent results as well as future challenges. The work contains a number of overviews of standard topics such as exactly solved lattice models and their various applications in statistical physics, from models of strongly correlated electrons to the conformational properties of polymer chains. It is equally wide ranging in its coverage of new directions and developing fields including quantum computers, financial markets, chaotic systems, Feigenbaum scaling, proteins, brain behaviour, immunology, Markov superposition, Bose-Einstein condensation, random matrices, exclusion statistics, vertex operator algebras and D-unsolvability.The level of coverage is appropriate for graduate students. It will be equally of interest to professional physicists who want to learn about progress in statistical physics in recent years. Experts will find this work useful because of its broad sweep of topics and its discussion of remaining unsolved problems.