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Application of Integrable Systems to Phase Transitions

Application of Integrable Systems to Phase Transitions PDF Author: C.B. Wang
Publisher: Springer Science & Business Media
ISBN: 3642385656
Category : Mathematics
Languages : en
Pages : 222

Book Description
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.

Application of Integrable Systems to Phase Transitions

Application of Integrable Systems to Phase Transitions PDF Author: C.B. Wang
Publisher: Springer Science & Business Media
ISBN: 3642385656
Category : Mathematics
Languages : en
Pages : 222

Book Description
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.

Symmetries and Algebraic Structures in Physics: Integral systems, solid state physics and theory of phase transitions

Symmetries and Algebraic Structures in Physics: Integral systems, solid state physics and theory of phase transitions PDF Author: V. V. Dodonov
Publisher: Nova Publishers
ISBN: 9781560720386
Category : Mathematics
Languages : en
Pages : 338

Book Description


Phase Transitions and Critical Phenomena

Phase Transitions and Critical Phenomena PDF Author:
Publisher: Elsevier
ISBN: 0080538762
Category : Science
Languages : en
Pages : 517

Book Description
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.

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 PDF Author: Geoffrey Grinstein
Publisher: World Scientific
ISBN: 9814513601
Category : Science
Languages : en
Pages : 270

Book Description
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.

Random Graphs, Phase Transitions, and the Gaussian Free Field

Random Graphs, Phase Transitions, and the Gaussian Free Field PDF Author: Martin T. Barlow
Publisher: Springer Nature
ISBN: 3030320111
Category : Mathematics
Languages : en
Pages : 421

Book Description
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.

Classical and Quantum Nonlinear Integrable Systems

Classical and Quantum Nonlinear Integrable Systems PDF Author: A Kundu
Publisher: CRC Press
ISBN: 9781420034615
Category : Science
Languages : en
Pages : 320

Book Description
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 PDF Author: Pavel Bleher
Publisher: Cambridge University Press
ISBN: 9780521802093
Category : Mathematics
Languages : en
Pages : 454

Book Description
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 PDF Author: Pei Dang
Publisher: Birkhäuser
ISBN: 3319488120
Category : Mathematics
Languages : en
Pages : 615

Book Description
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 PDF Author: Amit Dutta
Publisher: Cambridge University Press
ISBN: 1107068797
Category : Science
Languages : en
Pages : 357

Book Description
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 PDF Author: Jinho Baik
Publisher: American Mathematical Soc.
ISBN: 0821842404
Category : Mathematics
Languages : en
Pages : 448

Book Description
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.