03621nam 2200757Ia 450 991082331470332120200520144314.01-107-15343-31-280-48005-X97866104800500-511-16868-30-511-16911-60-511-16769-50-511-31455-80-511-61680-50-511-16823-3(CKB)1000000000352536(EBL)266152(OCoLC)173610031(SSID)ssj0000251071(PQKBManifestationID)11228914(PQKBTitleCode)TC0000251071(PQKBWorkID)10248321(PQKB)10794613(UkCbUP)CR9780511616808(MiAaPQ)EBC266152(Au-PeEL)EBL266152(CaPaEBR)ebr10130426(CaONFJC)MIL48005(PPN)137614993(EXLCZ)99100000000035253620060818d2006 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierStatistical mechanics of disordered systems a mathematical perspective /Anton Bovier1st ed.Cambridge, UK Cambridge University Press20061 online resource (xiv, 312 pages) digital, PDF file(s)Cambridge series in statistical and probabilistic mathematics ;[18]Title from publisher's bibliographic system (viewed on 05 Oct 2015).1-107-40533-5 0-521-84991-8 Includes bibliographical references (p. [297]-308) and index.Principles of statistical mechanics -- Lattice gases and spin systems -- Gibbsian formalism for lattice spin systems -- Cluster expansions -- Gibbsian formalism and metastates -- The random-field Ising model -- Disordered mean-field models -- The random energy model -- Derrida's generalized random energy models -- The SK models and the Parisi solution -- Hopfield models -- The number partitioning problem.This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail.Cambridge series on statistical and probabilistic mathematics ;18.Statistical mechanicsMathematical statisticsProbabilitiesSystem theoryStatistical mechanics.Mathematical statistics.Probabilities.System theory.519.5Bovier Anton1957-300719MiAaPQMiAaPQMiAaPQBOOK9910823314703321Statistical mechanics of disordered systems1099248UNINA