Application of Integrable Systems to Phase Transitions

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Applied
Cover of the book Application of Integrable Systems to Phase Transitions by C.B. Wang, Springer Berlin Heidelberg
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Author: C.B. Wang ISBN: 9783642385650
Publisher: Springer Berlin Heidelberg Publication: July 20, 2013
Imprint: Springer Language: English
Author: C.B. Wang
ISBN: 9783642385650
Publisher: Springer Berlin Heidelberg
Publication: July 20, 2013
Imprint: Springer
Language: English

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.

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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.

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