Application of Integrable Systems to Phase Transitions

  • C.B. Wang

Table of contents

  1. Front Matter
    Pages I-X
  2. C. B. Wang
    Pages 1-20
  3. C. B. Wang
    Pages 21-44
  4. C. B. Wang
    Pages 107-130
  5. C. B. Wang
    Pages 131-159
  6. Back Matter
    Pages 191-219

About this book

Introduction

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.

Keywords

Integrable system Large-N asymptotics Matrix model Phase transition Planar diagram Power-law Seiberg-Witten theory String equation Toda lattice Unified model

Authors and affiliations

  • C.B. Wang
    • 1
  1. 1.Institute of AnalysisTroyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-38565-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-38564-3
  • Online ISBN 978-3-642-38565-0
  • About this book
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