Title: Rigorous Results in the Sherrington–Kirkpatrick Model
Abstract: Spin Glass Theory and Far Beyond, pp. 635-656 (2023) No AccessChapter 30: Rigorous Results in the Sherrington–Kirkpatrick ModelWei-Kuo Chen, Dmitry Panchenko, and Francesco GuerraWei-Kuo ChenSchool of Mathematics, University of Minnesota, USA, Dmitry PanchenkoDepartment of Mathematics, University of Toronto, Canada, and Francesco GuerraDepartment of Physics, Sapienza University of Rome, Italyhttps://doi.org/10.1142/9789811273926_0030Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: Since the proposal of the solution of the SK model by Giorgio Parisi, the mathematical community has investigated the rigorous foundations of the results obtained by means of the replica method: this chapter focuses on some of the outcomes of such investigations. In the first part, Wei-Kuo Chen discusses the Parisi formula for the free energy of the SK model, the stability of the replica-symmetric solution, and the most recent results on disorder chaos. In the second part, Dmitry Panchenko reviews the central concept of ultrametricity, its relation with the Ghirlanda–Guerra identities in a large class of spin systems, and its implications on their landscape structure. Finally, in the last part, Francesco Guerra overviews the interpolating method for the SK model and the REM, and the emergent variational principle associated to these models. FiguresReferencesRelatedDetails Recommended Spin Glass Theory and Far BeyondMetrics History PDF download
Publication Year: 2023
Publication Date: 2023-08-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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