Phase Transitions Of Interacting Particle Systems

Author : Norio Konno
Publisher : World Scientific
ISBN 13 : 9814501182
Total Pages : 245 pages
Book Rating : 4.87/5 ( download)

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Download or read book Phase Transitions Of Interacting Particle Systems written by Norio Konno and published by World Scientific. This book was released on 1995-01-16 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, interacting particle systems have been studied widely from the standpoints of mathematics, physics, chemistry and biology. Many researchers are becoming interested in this field.This book focuses on the phase transitions of interacting particle systems, especially their critical values and order parameters. It poses the following question: How can we get good bounds on the critical values and the order parameters? This question is very basic, and many researchers have been trying to get better bounds rigorously. Hence the book provides bounds — both the author's and others'.

Author : T.M. Liggett
Publisher : Springer Science & Business Media
ISBN 13 : 1461385423
Total Pages : 499 pages
Book Rating : 4.24/5 ( download)

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Download or read book Interacting Particle Systems written by T.M. Liggett and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: At what point in the development of a new field should a book be written about it? This question is seldom easy to answer. In the case of interacting particle systems, important progress continues to be made at a substantial pace. A number of problems which are nearly as old as the subject itself remain open, and new problem areas continue to arise and develop. Thus one might argue that the time is not yet ripe for a book on this subject. On the other hand, this field is now about fifteen years old. Many important of several basic models is problems have been solved and the analysis almost complete. The papers written on this subject number in the hundreds. It has become increasingly difficult for newcomers to master the proliferating literature, and for workers in allied areas to make effective use of it. Thus I have concluded that this is an appropriate time to pause and take stock of the progress made to date. It is my hope that this book will not only provide a useful account of much of this progress, but that it will also help stimulate the future vigorous development of this field.

Author : Richard Durrett
Publisher : American Mathematical Soc.
ISBN 13 : 0821850423
Total Pages : 394 pages
Book Rating : 4.28/5 ( download)

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Download or read book Particle Systems, Random Media and Large Deviations written by Richard Durrett and published by American Mathematical Soc.. This book was released on 1985 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the proceedings of the 1984 AMS Summer Research Conference. This work provides a summary of results from some of the areas in probability theory; interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations.

Author : Mufa Chen
Publisher : World Scientific
ISBN 13 : 9812388117
Total Pages : 610 pages
Book Rating : 4.17/5 ( download)

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Download or read book From Markov Chains to Non-equilibrium Particle Systems written by Mufa Chen and published by World Scientific. This book was released on 2004 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is representative of the work of Chinese probabilists on probability theory and its applications in physics. It presents a unique treatment of general Markov jump processes: uniqueness, various types of ergodicity, Markovian couplings, reversibility, spectral gap, etc. It also deals with a typical class of non-equilibrium particle systems, including the typical Schlögl model taken from statistical physics. The constructions, ergodicity and phase transitions for this class of Markov interacting particle systems, namely, reaction-diffusion processes, are presented. In this new edition, a large part of the text has been updated and two-and-a-half chapters have been rewritten. The book is self-contained and can be used in a course on stochastic processes for graduate students.

Author : G.R. Grimmett
Publisher : Springer Science & Business Media
ISBN 13 : 9401583269
Total Pages : 334 pages
Book Rating : 4.68/5 ( download)

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Download or read book Probability and Phase Transition written by G.R. Grimmett and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability. The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

Author : Daniel C. Cabra
Publisher : Springer Science & Business Media
ISBN 13 : 3642104487
Total Pages : 380 pages
Book Rating : 4.80/5 ( download)

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Download or read book Modern Theories of Many-Particle Systems in Condensed Matter Physics written by Daniel C. Cabra and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Condensed matter systems where interactions are strong are inherently difficult to analyze theoretically. The situation is particularly interesting in low-dimensional systems, where quantum fluctuations play a crucial role. Here, the development of non-perturbative methods and the study of integrable field theory have facilitated the understanding of the behavior of many quasi one- and two-dimensional strongly correlated systems. In view of the same rapid development that has taken place for both experimental and numerical techniques, as well as the emergence of novel testing-grounds such as cold atoms or graphene, the current understanding of strongly correlated condensed matter systems differs quite considerably from standard textbook presentations. The present volume of lecture notes aims to fill this gap in the literature by providing a collection of authoritative tutorial reviews, covering such topics as quantum phase transitions of antiferromagnets and cuprate-based high-temperature superconductors, electronic liquid crystal phases, graphene physics, dynamical mean field theory applied to strongly correlated systems, transport through quantum dots, quantum information perspectives on many-body physics, frustrated magnetism, statistical mechanics of classical and quantum computational complexity, and integrable methods in statistical field theory. As both graduate-level text and authoritative reference on this topic, this book will benefit newcomers and more experienced researchers in this field alike.

Author : Matthias Birkner
Publisher : World Scientific
ISBN 13 : 9811206104
Total Pages : 363 pages
Book Rating : 4.08/5 ( download)

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Download or read book Genealogies Of Interacting Particle Systems written by Matthias Birkner and published by World Scientific. This book was released on 2020-02-24 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interacting particle systems are Markov processes involving infinitely many interacting components. Since their introduction in the 1970s, researchers have found many applications in statistical physics and population biology. Genealogies, which follow the origin of the state of a site backwards in time, play an important role in their studies, especially for the biologically motivated systems.The program Genealogies of Interacting Particle Systems held at the Institute for Mathematical Sciences, National University of Singapore, from 17 July to 18 Aug 2017, brought together experts and young researchers interested in this modern topic. Central to the program were learning sessions where lecturers presented work outside of their own research, as well as a normal workshop. This is reflected in the present volume which contains two types of articles:Written by respected researchers, including experts in the field such as Steve Evans, member of the US National Academy of Sciences, as well as Anton Wakolbinger, Andreas Greven, and many others, this volume will no doubt be a valuable contribution to the probability community.

Author : Matthias Birkner
Publisher : World Scientific
ISBN 13 : 9811206090
Total Pages : 363 pages
Book Rating : 4.92/5 ( download)

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Download or read book Genealogies of Interacting Particle Systems written by Matthias Birkner and published by World Scientific. This book was released on 2020 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Interacting particle systems are Markov processes involving infinitely many interacting components. Since their introduction in the 1970s, researchers have found many applications in statistical physics and population biology. Genealogies, which follow the origin of the state of a site backwards in time, play an important role in their studies, especially for the biologically motivated systems. The program Genealogies of Interacting Particle Systems held at the Institute for Mathematical Sciences, National University of Singapore, from 17 July to 18 Aug 2017, brought together experts and young researchers interested in this modern topic. Central to the program were learning sessions where lecturers presented work outside of their own research, as well as a normal workshop "--Publisher's website.

Author : Thomas M. Liggett
Publisher : Springer Science & Business Media
ISBN 13 : 3662039907
Total Pages : 346 pages
Book Rating : 4.08/5 ( download)

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Download or read book Stochastic Interacting Systems: Contact, Voter and Exclusion Processes written by Thomas M. Liggett and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interactive particle systems is a branch of probability theory with close connections to mathematical physics and mathematical biology. This book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. It explains and develops many of the most useful techniques in the field.

Author : Taiki Haga
Publisher : Springer
ISBN 13 : 9811361711
Total Pages : 156 pages
Book Rating : 4.15/5 ( download)

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Download or read book Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems written by Taiki Haga and published by Springer. This book was released on 2019-01-24 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates phase transitions and critical phenomena in disordered systems driven out of equilibrium. First, the author derives a dimensional reduction property that relates the long-distance physics of driven disordered systems to that of lower dimensional pure systems. By combining this property with a modern renormalization group technique, the critical behavior of random field spin models driven at a uniform velocity is subsequently investigated. The highlight of this book is that the driven random field XY model is shown to exhibit the Kosterlitz–Thouless transition in three dimensions. This is the first example of topological phase transitions in which the competition between quenched disorder and nonequilibrium driving plays a crucial role. The book also includes a pedagogical review of a renormalizaion group technique for disordered systems.