LEADER 02766oam 2200541 450 001 9910437879603321 005 20190911112726.0 010 $a3-642-38565-6 024 7 $a10.1007/978-3-642-38565-0 035 $a(OCoLC)853663817 035 $a(MiFhGG)GVRL6UOH 035 $a(EXLCZ)992670000000533791 100 $a20130718d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aApplication of integrable systems to phase transitions /$fC.B. Wang 205 $a1st ed. 2013. 210 1$aHeidelberg, Germany :$cSpringer,$d2013. 215 $a1 online resource (x, 219 pages) $cillustrations 225 0 $aGale eBooks 300 $aDescription based upon print version of record. 311 $a3-642-38564-8 311 $a3-642-44024-X 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 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. 330 $aThe 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. 606 $aPhase transformations (Statistical physics) 606 $aEigenfunctions 606 $aMatrix analytic methods 606 $aQuantum theory$xMathematics 615 0$aPhase transformations (Statistical physics) 615 0$aEigenfunctions. 615 0$aMatrix analytic methods. 615 0$aQuantum theory$xMathematics. 676 $a510 676 $a515.5 676 $a519 676 $a530.15 700 $aWang$b C.B$4aut$4http://id.loc.gov/vocabulary/relators/aut$01061514 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910437879603321 996 $aApplication of Integrable Systems to Phase Transitions$92518998 997 $aUNINA