1. Introduction -- 2. Densities in Hermitian matrix models -- 3. Bifurcation transitions and expansions -- 4. Large-N transitions and critical phenomena -- 5. Densities in unitary matrix models -- 6. Transitions in the unitary matrix models -- 7. Marcenko-Pastur distribution and McKay's law
Summary
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
