TY  - BOOK
AU  - Wang,C.B.
TI  - Application of integrable systems to phase transitions
SN  - 9783642385643 (hardcover : alk. paper)
U1  - 530.414 23
PY  - 2013///
CY  - Berlin :     
PB  - Springer-Verlag,  
KW  - Phase transformations (Statistical physics).
KW  - Eigenfunctions.
KW  - Matrix analytic methods
N1  - Includes index; 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--
Appendices--
Index
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
ER  -