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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