02766oam 2200541 450 001001700000005001700017010001800034024003000052035002100082035002100103035003000124100004000154101000800194135001800202181000800220182000600228183000700234200007200241205001800313210004400331215005300375225001600428300005200444311001900496311001900515320005100534327027800585330086500863606004801728606001901776606002801795606003201823615004801855615002001903615002901923615003301952676000801985676001001993676000802003676001102011700007202022801001102094801001102105906000902116912002102125996006802146997001002214991043787960332120190911112726.0 a3-642-38565-67 a10.1007/978-3-642-38565-0 a(OCoLC)853663817 a(MiFhGG)GVRL6UOH a(EXLCZ)992670000000533791 a20130718d2013 uy 00 aeng aurun|---uuuua ctxt cc acr10aApplication of integrable systems to phase transitions /fC.B. Wang a1st ed. 2013. 1aHeidelberg, Germany :cSpringer,d2013. a1 online resource (x, 219 pages) cillustrations0 aGale eBooks aDescription based upon print version of record. a3-642-38564-8 a3-642-44024-X aIncludes bibliographical references and index. 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. 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. aPhase transformations (Statistical physics) aEigenfunctions aMatrix analytic methods aQuantum theoryxMathematics 0aPhase transformations (Statistical physics) 0aEigenfunctions. 0aMatrix analytic methods. 0aQuantum theoryxMathematics. a510 a515.5 a519 a530.15 aWangb C.B4aut4http://id.loc.gov/vocabulary/relators/aut01061514 0bMiFhGG 1bMiFhGG aBOOK a9910437879603321 aApplication of Integrable Systems to Phase Transitions92518998 aUNINA