Application of Integrable Systems to Phase Transitions, 1st Edition

  • Published By:
  • ISBN-10: 3642385656
  • ISBN-13: 9783642385650
  • DDC: 530.414
  • Grade Level Range: College Freshman - College Senior
  • 219 Pages | eBook
  • Original Copyright 2013 | Published/Released May 2014
  • This publication's content originally published in print form: 2013

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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.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
1: Introduction.
2: Densities in Hermitian Matrix Models.
3: Bifurcation Transitions and Expansions.
4: Large-N Transitions and Critical Phenomena.
5: Densities in Unitary Matrix Models.
6: Transitions in the Unitary Matrix Models.
7: Marcenko-Pastur Distribution and McKay's Law.
Some Integral Formulas.
Properties of the Elliptic Integrals.
Lax Pairs Based on the Potentials.
Hypergeometric-Type Differential Equations.