Application of Integrable Systems to Phase Transitions
Application of Integrable Systems to Phase Transitions

Author: C.B. Wang

Publisher: Springer Science & Business Media

Published: 2013-07-20

Total Pages: 222

ISBN-13: 3642385656

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The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems. Many new density models and free energy functions are consequently solved and presented. The phase transition models including critical phenomena with fractional power-law for the discontinuities of the free energies in the matrix models are systematically classified by means of a clear and rigorous mathematical demonstration. The methods here will stimulate new research directions such as the important Seiberg-Witten differential in Seiberg-Witten theory for solving the mass gap problem in quantum Yang-Mills theory. The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and Seiberg-Witten theory.

Phase Transitions and Critical Phenomena
Phase Transitions and Critical Phenomena

Author:

Publisher: Elsevier

Published: 2000-09-21

Total Pages: 517

ISBN-13: 0080538762

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The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies.Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations.The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.

Random Graphs, Phase Transitions, and the Gaussian Free Field
Random Graphs, Phase Transitions, and the Gaussian Free Field

Author: Martin T. Barlow

Publisher: Springer Nature

Published: 2019-12-03

Total Pages: 421

ISBN-13: 3030320111

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The 2017 PIMS-CRM Summer School in Probability was held at the Pacific Institute for the Mathematical Sciences (PIMS) at the University of British Columbia in Vancouver, Canada, during June 5-30, 2017. It had 125 participants from 20 different countries, and featured two main courses, three mini-courses, and twenty-nine lectures. The lecture notes contained in this volume provide introductory accounts of three of the most active and fascinating areas of research in modern probability theory, especially designed for graduate students entering research: Scaling limits of random trees and random graphs (Christina Goldschmidt) Lectures on the Ising and Potts models on the hypercubic lattice (Hugo Duminil-Copin) Extrema of the two-dimensional discrete Gaussian free field (Marek Biskup) Each of these contributions provides a thorough introduction that will be of value to beginners and experts alike.

Directions In Condensed Matter Physics: Memorial Volume In Honor Of Shang-keng Ma
Directions In Condensed Matter Physics: Memorial Volume In Honor Of Shang-keng Ma

Author: Geoffrey Grinstein

Publisher: World Scientific

Published: 1986-08-01

Total Pages: 270

ISBN-13: 9814513601

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This volume collects several in-depth articles giving lucid discussions on new developments in statistical and condensed matter physics. Many, though not all, contributors had been in touch with the late S-K Ma. Written by some of the world's experts and originators of new ideas in the field, this book is a must for all researchers in theoretical physics. Most of the articles should be accessible to diligent graduate students and experienced readers will gain from the wealth of materials contained herein.

Classical and Quantum Nonlinear Integrable Systems
Classical and Quantum Nonlinear Integrable Systems

Author: A Kundu

Publisher: CRC Press

Published: 2019-04-23

Total Pages: 320

ISBN-13: 9781420034615

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Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories

Random Matrix Models and Their Applications
Random Matrix Models and Their Applications

Author: Pavel Bleher

Publisher: Cambridge University Press

Published: 2001-06-04

Total Pages: 454

ISBN-13: 9780521802093

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Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.

New Trends in Analysis and Interdisciplinary Applications
New Trends in Analysis and Interdisciplinary Applications

Author: Pei Dang

Publisher: Birkhäuser

Published: 2017-04-18

Total Pages: 615

ISBN-13: 3319488120

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This book presents a collection of papers from the 10th ISAAC Congress 2015, held in Macau, China. The papers, prepared by respected international experts, address recent results in Mathematics, with a special focus on Analysis. By structuring the content according to the various mathematical topics, the volume offers specialists and non-specialists alike an excellent source of information on the state-of-the-art in Mathematical Analysis and its interdisciplinary applications.

Quantum Phase Transitions in Transverse Field Models
Quantum Phase Transitions in Transverse Field Models

Author: Amit Dutta

Publisher: Cambridge University Press

Published: 2015-01-28

Total Pages: 357

ISBN-13: 1107068797

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This book establishes the fundamental connections between the physics of quantum phase transitions and the technological promise of quantum information.

Integrable Systems and Random Matrices
Integrable Systems and Random Matrices

Author: Jinho Baik

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 448

ISBN-13: 0821842404

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This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa-Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann-Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems.