Application of Integrable Systems to Phase Transitions

Authors: Wang, C.B.

  • 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
see more benefits

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-3-642-38565-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-642-38564-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-642-44024-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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.

About the authors

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

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)

Table of contents (7 chapters)

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-3-642-38565-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-642-38564-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-642-44024-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Application of Integrable Systems to Phase Transitions
Authors
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-38565-0
DOI
10.1007/978-3-642-38565-0
Hardcover ISBN
978-3-642-38564-3
Softcover ISBN
978-3-642-44024-3
Edition Number
1
Number of Pages
X, 219
Topics