Download or read book Planar Ising Correlations written by John Palmer and published by Springer Science & Business Media. This book was released on 2007-06-15 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steady progress in recent years has been made in understanding the special mathematical features of certain exactly solvable models in statistical mechanics and quantum field theory, including the scaling limits of the 2-D Ising (lattice) model, and more generally, a class of 2-D quantum fields known as holonomic fields. New results have made it possible to obtain a detailed nonperturbative analysis of the multi-spin correlations. In particular, the book focuses on deformation analysis of the scaling functions of the Ising model, and will appeal to graduate students, mathematicians, and physicists interested in the mathematics of statistical mechanics and quantum field theory.
Download or read book Planar Ising Correlations written by Anne Boutet de Monvel and published by . This book was released on 2007 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines in detail the correlations for the two-dimensional Ising model in the infinite volume or thermodynamic limit and the sub- and super-critical continuum scaling limits. Steady progress in recent years has been made in understanding the special mathematical features of certain exactly solvable models in statistical mechanics and quantum field theory, including the scaling limits of the 2-D Ising (lattice) model, and more generally, a class of 2-D quantum fields known as holonomic fields. New results have made it possible to obtain a detailed nonperturbative analysis of the multi-spin correlations. In particular, the book focuses on deformation analysis of the scaling functions of the Ising model. This self-contained work also includes discussions on Pfaffians, elliptic uniformization, the Grassmann calculus for spin representations, Weiner--Hopf factorization, determinant bundles, and monodromy preserving deformations. This work explores the Ising model as a microcosm of the confluence of interesting ideas in mathematics and physics, and will appeal to graduate students, mathematicians, and physicists interested in the mathematics of statistical mechanics and quantum field theory.
Download or read book Learning Planar Ising Models written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus our attention on the class of planar Ising models, for which inference is tractable using techniques of statistical physics [Kac and Ward; Kasteleyn]. Based on these techniques and recent methods for planarity testing and planar embedding [Chrobak and Payne], we propose a simple greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. We present the results of numerical experiments evaluating the performance of our algorithm.
Download or read book XVIIth International Congress on Mathematical Physics written by Arne Jensen and published by World Scientific. This book was released on 2014 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals.
Download or read book The Riemann Problem Complete Integrability and Arithmetic Applications written by D. Chudnovsky and published by Springer. This book was released on 2006-11-14 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seminar on the Riemann Problem, Complete Integrability and Arithmetic Applications
Download or read book The Two Dimensional Ising Model written by Barry M. McCoy and published by Courier Corporation. This book was released on 2014-04-23 with total page 484 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 Sojourns in Probability Theory and Statistical Physics II written by Vladas Sidoravicius and published by Springer Nature. This book was released on 2019-10-17 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.
Download or read book Exactly Solved Models in Statistical Mechanics written by Rodney J. Baxter and published by Elsevier. This book was released on 2016-06-12 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exactly Solved Models in Statistical Mechanics
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 484 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 MathPhys Odyssey 2001 written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'MathPhys Odyssey 2001' will serve as an excellent reference text for mathematical physicists and graduate students in a number of areas.; Kashiwara/Miwa have a good track record with both SV and Birkhauser.
Download or read book Statistical Mechanics And Field Theory Proceedings Of The Seventh Physics Summer School written by Bazhanov Vladimir V and published by World Scientific. This book was released on 1995-12-21 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume aims to expose graduate students to the basic ideas of field theory and statistical mechanics and to give them an understanding and appreciation of current topical research.
Download or read book Exactly Soluble Models In Statistical Mechanics Historical Perspectives And Current Status written by Christopher King and published by World Scientific. This book was released on 1997-02-26 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Doing Mathematics Convention Subject Calculation Analogy 2nd Edition written by Martin H Krieger and published by World Scientific. This book was released on 2015-01-15 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doing Mathematics discusses some ways mathematicians and mathematical physicists do their work and the subject matters they uncover and fashion. The conventions they adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies they discover and employ, all depend on the mathematics — what will work out and what won't. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connections between algebra and topology, and the series of rigorous proofs of the stability of matter. The many and varied solutions to the two-dimensional Ising model of ferromagnetism make sense as a whole when they are seen in an analogy developed by Richard Dedekind in the 1880s to algebraicize Riemann's function theory; by Robert Langlands' program in number theory and representation theory; and, by the analogy between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics. In effect, we begin to see 'an identity in a manifold presentation of profiles,' as the phenomenologists would say.This second edition deepens the particular examples; it describe the practical role of mathematical rigor; it suggests what might be a mathematician's philosophy of mathematics; and, it shows how an 'ugly' first proof or derivation embodies essential features, only to be appreciated after many subsequent proofs. Natural scientists and mathematicians trade physical models and abstract objects, remaking them to suit their needs, discovering new roles for them as in the recent case of the Painlevé transcendents, the Tracy-Widom distribution, and Toeplitz determinants. And mathematics has provided the models and analogies, the ordinary language, for describing the everyday world, the structure of cities, or God's infinitude.
Download or read book Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii iv Invited Lectures written by Rajendra Bhatia and published by World Scientific. This book was released on 2011-06-06 with total page 4137 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Download or read book Proceedings of the International Congress of Mathematicians 2010 icm 2010 in 4 Volumes Vol I Plenary Lectures and Ceremonies Vols Ii iv Invited Lectures written by and published by World Scientific. This book was released on 2011 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis Complex Geometry and Mathematical Physics written by Paul M. N. Feehan and published by American Mathematical Soc.. This book was released on 2015-07-21 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Analysis, Complex Geometry and Mathematical Physics: In Honor of Duong H. Phong, which was held from May 7-11, 2013, at Columbia University, New York. The conference featured thirty speakers who spoke on a range of topics reflecting the breadth and depth of the research interests of Duong H. Phong on the occasion of his sixtieth birthday. A common thread, familiar from Phong's own work, was the focus on the interplay between the deep tools of analysis and the rich structures of geometry and physics. Papers included in this volume cover topics such as the complex Monge-Ampère equation, pluripotential theory, geometric partial differential equations, theories of integral operators, integrable systems and perturbative superstring theory.
Download or read book The Random Cluster Model written by Geoffrey R. Grimmett and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
