LEADER 02614nam 2200493 a 450 001 9910438147803321 005 20200520144314.0 010 $a1-299-33752-X 010 $a1-4614-6289-4 024 7 $a10.1007/978-1-4614-6289-7 035 $a(OCoLC)834548674 035 $a(MiFhGG)GVRL6YPB 035 $a(CKB)2550000001017944 035 $a(MiAaPQ)EBC1106188 035 $a(EXLCZ)992550000001017944 100 $a20130125d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 14$aThe Sherrington-Kirkpatrick model /$fDmitry Panchenko 205 $a1st ed. 2013. 210 $aNew York $cSpringer$dc2013 215 $a1 online resource (xii, 156 pages) 225 0$aSpringer monographs in mathematics,$x1439-7382 300 $a"ISSN: 1439-7382." 311 $a1-4899-9373-8 311 $a1-4614-6288-6 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1 The Free Energy and Gibbs Measure -- 2 The Ruelle Probability Cascades -- 3 The Parisi Formula -- 4 Toward a Generalized Parisi Ansatz -- A Appendix -- Bibliography -- Notes and Comments -- References -- Index. 330 $aThe celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays. 410 0$aSpringer monographs in mathematics. 606 $aSpin glasses$xMathematical models 615 0$aSpin glasses$xMathematical models. 676 $a538.4 700 $aPanchenko$b Dmitry$0791639 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438147803321 996 $aSherrington-Kirkpatrick model$91769641 997 $aUNINA