02766oam 2200541 450 991043787960332120190911112726.03-642-38565-610.1007/978-3-642-38565-0(OCoLC)853663817(MiFhGG)GVRL6UOH(EXLCZ)99267000000053379120130718d2013 uy 0engurun|---uuuuatxtccrApplication of integrable systems to phase transitions /C.B. Wang1st ed. 2013.Heidelberg, Germany :Springer,2013.1 online resource (x, 219 pages) illustrationsGale eBooksDescription based upon print version of record.3-642-38564-8 3-642-44024-X Includes bibliographical references and index.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.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.Phase transformations (Statistical physics)EigenfunctionsMatrix analytic methodsQuantum theoryMathematicsPhase transformations (Statistical physics)Eigenfunctions.Matrix analytic methods.Quantum theoryMathematics.510515.5519530.15Wang C.Bauthttp://id.loc.gov/vocabulary/relators/aut1061514MiFhGGMiFhGGBOOK9910437879603321Application of Integrable Systems to Phase Transitions2518998UNINA