Application of Integrable Systems to Phase Transitions

Wang, C.B.

Springer-Verlag Berlin and Heidelberg GmbH & Co. K（2015/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 219 p.
• 言語 ENG
• 商品コード 9783642440243

Full Description

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.

Contents

Introduction.- Densities in Hermitian Matrix Models.- Bifurcation Transitions and Expansions.- Large-N Transitions and Critical Phenomena.- Densities in Unitary Matrix Models.- Transitions in the Unitary Matrix Models.- Marcenko-Pastur Distribution and McKay's Law.