Application of integrable systems to phase transitions

✍ Scribed by C.B. Wang (auth.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 2013
Tongue: English
Leaves: 222
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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 Matter....Pages I-X
Introduction....Pages 1-20
Densities in Hermitian Matrix Models....Pages 21-44
Bifurcation Transitions and Expansions....Pages 45-74
Large-N Transitions and Critical Phenomena....Pages 75-106
Densities in Unitary Matrix Models....Pages 107-130
Transitions in the Unitary Matrix Models....Pages 131-159
Marcenko-Pastur Distribution and McKay’s Law....Pages 161-189
Back Matter....Pages 191-219

✦ Subjects

Mathematical Applications in the Physical Sciences; Special Functions; Mathematical Physics

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