Statistical Mechanics: Algorithms and Computations

Statistical Mechanics: Algorithms and Computations PDF

Author: Werner Krauth

Publisher: OUP Oxford

Published: 2006-09-14

Total Pages: 356

ISBN-13: 9780198515357

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This book discusses the computational approach in modern statistical physics, adopting simple language and an attractive format of many illustrations, tables and printed algorithms. The discussion of key subjects in classical and quantum statistical physics will appeal to students, teachers and researchers in physics and related sciences. The focus is on orientation with implementation details kept to a minimum. - ;This book discusses the computational approach in modern statistical physics in a clear and accessible way and demonstrates its close relation to other approaches in theoretical physics. Individual chapters focus on subjects as diverse as the hard sphere liquid, classical spin models, single quantum particles and Bose-Einstein condensation. Contained within the chapters are in-depth discussions of algorithms, ranging from basic enumeration methods to modern Monte Carlo techniques. The emphasis is on orientation, with discussion of implementation details kept to a minimum. Illustrations, tables and concise printed algorithms convey key information, making the material very accessible. The book is completely self-contained and graphs and tables can readily be reproduced, requiring minimal computer code. Most sections begin at an elementary level and lead on to the rich and difficult problems of contemporary computational and statistical physics. The book will be of interest to a wide range of students, teachers and researchers in physics and the neighbouring sciences. An accompanying CD allows incorporation of the book's content (illustrations, tables, schematic programs) into the reader's own presentations. - ;'This book is the best one I have reviewed all year.' Alan Hinchliffe, Physical Sciences Educational Reviews -

Statistical Mechanics: Algorithms and Computations

Statistical Mechanics: Algorithms and Computations PDF

Author: Werner Krauth

Publisher: OUP Oxford

Published: 2006-09-14

Total Pages: 360

ISBN-13: 0191523321

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This book discusses the computational approach in modern statistical physics in a clear yet accessible way, and works out its intimate relations with other approaches in theoretical physics. Individual chapters focus on subjects as diverse as the hard sphere liquid, classical spin models, single quantum particles and Bose-Einstein condensation. They contain in-depth discussions of algorithms ranging from basic enumeration methods to modern Monte Carlo techniques. The emphasis is on orientation. Discussions of implementation details are kept to a minimum. The book heavily relies on illustrations, tables and concise printed algorithms to convey key information: all the material remains easily accessible. The book is fully self-contained: graphs and tables can be readily reproduced by programming at most a few dozen lines of computer code. Most sections lead from an elementary discussion to the rich and difficult problems of contemporary computational and statistical physics, and will be of interest to a wide range of students, teachers and researchers in physics and the neighboring sciences. An accompanying CD allows to incorporate the layout material (illustrations, tables, schematic programs) into the reader's own presentations.

Advanced Statistical Mechanics

Advanced Statistical Mechanics PDF

Author: Barry M McCoy

Publisher: Oxford University Press

Published: 2010

Total Pages: 641

ISBN-13: 0199556636

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McCoy presents the advances made in statistical mechanics over the last 50 years, including mathematical theorems on order and phase transitions, numerical and series computations of phase diagrams and solutions for important solvable models such as Ising and 8 vortex.

Computational Statistical Mechanics

Computational Statistical Mechanics PDF

Author: W.G. Hoover

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 330

ISBN-13: 0444596593

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Computational Statistical Mechanics describes the use of fast computers to simulate the equilibrium and nonequilibrium properties of gases, liquids, and solids at, and away from equilibrium. The underlying theory is developed from basic principles and illustrated by applying it to the simplest possible examples. Thermodynamics, based on the ideal gas thermometer, is related to Gibb's statistical mechanics through the use of Nosé-Hoover heat reservoirs. These reservoirs use integral feedback to control temperature. The same approach is carried through to the simulation and analysis of nonequilibrium mass, momentum, and energy flows. Such a unified approach makes possible consistent mechanical definitions of temperature, stress, and heat flux which lead to a microscopic demonstration of the Second Law of Thermodynamics directly from mechanics. The intimate connection linking Lyapunov-unstable microscopic motions to macroscopic dissipative flows through multifractal phase-space structures is illustrated with many examples from the recent literature. The book is well-suited for undergraduate courses in advanced thermodynamics, statistical mechanic and transport theory, and graduate courses in physics and chemistry.

Statistical Mechanics

Statistical Mechanics PDF

Author: James Sethna

Publisher: OUP Oxford

Published: 2006-04-07

Total Pages: 374

ISBN-13: 0191566217

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In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.

Computational Statistical Physics

Computational Statistical Physics PDF

Author: Lucas Böttcher

Publisher: Cambridge University Press

Published: 2021-08-26

Total Pages: 275

ISBN-13: 9781108841429

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Providing a detailed and pedagogical account of the rapidly-growing field of computational statistical physics, this book covers both the theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational applications such as percolation, random walks, magnetic systems, machine learning dynamics, and spreading processes on complex networks. A detailed discussion of molecular dynamics simulations is also included, a topic of great importance in biophysics and physical chemistry. The accessible and self-contained approach adopted by the authors makes this book suitable for teaching courses at graduate level, and numerous worked examples and end of chapter problems allow students to test their progress and understanding.

Information, Physics, and Computation

Information, Physics, and Computation PDF

Author: Marc Mézard

Publisher: Oxford University Press

Published: 2009-01-22

Total Pages: 584

ISBN-13: 019857083X

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A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

Statistical Approach to Quantum Field Theory

Statistical Approach to Quantum Field Theory PDF

Author: Andreas Wipf

Publisher: Springer Nature

Published: 2021-10-25

Total Pages: 568

ISBN-13: 3030832635

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This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.

Statistical Mechanics

Statistical Mechanics PDF

Author: A. J. Berlinsky

Publisher: Springer Nature

Published: 2019-10-03

Total Pages: 602

ISBN-13: 3030281876

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In a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph.D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects. The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson’s epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods due to Anderson, Kosterlitz, Thouless and Young. Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.