TY  - BOOK
AU  - Wang,C.B.
ED  - SpringerLink (Online service)
TI  - Application of Integrable Systems to Phase Transitions
SN  - 9783642385650
AV  - QC19.2-20.85 
U1  - 519 23
PY  - 2013///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Springer
KW  - Mathematics
KW  - Special functions
KW  - Mathematical physics
KW  - Mathematical Applications in the Physical Sciences
KW  - Special Functions
KW  - Mathematical Physics
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-642-38565-0
ER  -