Application of Integrable Systems to Phase Transitions
2013, X, 219 p. 10 illus.
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First book in the field of matrix models to apply integrable systems to solve the phase transition problems
The only book to date to provide a unified model for the densities of eigenvalues in quantum chromodynamics (QCD)
An application book but with rigorous mathematical proofs to present a systematic classification of phase transition models in the momentum aspect
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.
Content Level »Research
Keywords »Integrable system - Large-N asymptotics - Matrix model - Phase transition - Planar diagram - Power-law - Seiberg-Witten theory - String equation - Toda lattice - Unified model