Overview
- First book in the field of matrix models to apply integrable systems to solve the phase transition problems
- The only book to date to provide a unified model for the densities of eigenvalues in quantum chromodynamics (QCD)
- An application book but with rigorous mathematical proofs to present a systematic classification of phase transition models in the momentum aspect
- Includes supplementary material: sn.pub/extras
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Table of contents (7 chapters)
Keywords
About this book
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.
Reviews
From the book reviews:
“The author addresses a large variety of integrable systems, their remarkable connections to orthogonal polynomials and to string equations, and the ensuing consequences for the associated free energies and critical behavior near phase transitions. This text contains much useful information and relevant techniques for researchers interested in specific integrable model systems whose features might be of relevance for some aspects of fundamental particle theory.” (Uwe C. Täuber, Mathematical Reviews, July, 2014)Authors and Affiliations
About the author
The author obtained his Ph.D in mathematics at University of Pittsburgh in 1998. Then he worked at University of California, Davis, as a visiting research assistant professor for one year before he started working in industry. The Marcenko-Pastur distribution in econophysics inspired him to search a unified model for the eigenvalue densities in the matrix models. The phase transition models discussed in this book are based on the Gross-Witten third-order phase transition model and the researches on transition problems in complex systems and data clustering. He is now a data scientist at Institute of Analysis, MI, USA. Email: chiebingwang@yahoo.com
Bibliographic Information
Book Title: Application of Integrable Systems to Phase Transitions
Authors: C.B. Wang
DOI: https://doi.org/10.1007/978-3-642-38565-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2013
Hardcover ISBN: 978-3-642-38564-3Published: 30 July 2013
Softcover ISBN: 978-3-642-44024-3Published: 09 August 2015
eBook ISBN: 978-3-642-38565-0Published: 20 July 2013
Edition Number: 1
Number of Pages: X, 219
Topics: Mathematical Applications in the Physical Sciences, Special Functions, Mathematical Physics