Statistical mechanics of disordered systems: a mathematical perspective
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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2006
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| Schriftenreihe: | Cambridge series on statistical and probabilistic mathematics
18 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 Online-Ressource (xiv, 312 Seiten) |
| ISBN: | 9780511616808 |
| DOI: | 10.1017/CBO9780511616808 |
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| 245 | 1 | 0 | |a Statistical mechanics of disordered systems |b a mathematical perspective |c Anton Bovier ; Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin and Institut für Mathematik, Technsiche Universität Berlin |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a 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 | |
| 520 | |a 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 | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Bovier, Anton 1957- |
| author_GND | (DE-588)109223829 |
| author_facet | Bovier, Anton 1957- |
| author_role | aut |
| author_sort | Bovier, Anton 1957- |
| author_variant | a b ab |
| building | Verbundindex |
| bvnumber | BV043940900 |
| classification_rvk | UG 3900 SK 950 |
| collection | ZDB-20-CBO |
| contents | 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511616808 (OCoLC)699187930 (DE-599)BVBBV043940900 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511616808 |
| format | Electronic eBook |
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| id | DE-604.BV043940900 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9780511616808 |
| language | English |
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| oclc_num | 699187930 |
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| physical | 1 Online-Ressource (xiv, 312 Seiten) |
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| publishDate | 2006 |
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| spelling | Bovier, Anton 1957- (DE-588)109223829 aut Statistical mechanics of disordered systems a mathematical perspective Anton Bovier ; Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin and Institut für Mathematik, Technsiche Universität Berlin Cambridge Cambridge University Press 2006 © 2010 1 Online-Ressource (xiv, 312 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge series on statistical and probabilistic mathematics 18 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Statistical mechanics Mathematical statistics Probabilities System theory Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Ungeordnetes System (DE-588)4124353-5 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Ungeordnetes System (DE-588)4124353-5 s Statistische Mechanik (DE-588)4056999-8 s Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-84991-3 Erscheint auch als Druck-Ausgabe 978-1-107-40533-2 https://doi.org/10.1017/CBO9780511616808 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bovier, Anton 1957- Statistical mechanics of disordered systems a mathematical perspective 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 Statistical mechanics Mathematical statistics Probabilities System theory Mathematische Physik (DE-588)4037952-8 gnd Ungeordnetes System (DE-588)4124353-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4124353-5 (DE-588)4056999-8 |
| title | Statistical mechanics of disordered systems a mathematical perspective |
| title_auth | Statistical mechanics of disordered systems a mathematical perspective |
| title_exact_search | Statistical mechanics of disordered systems a mathematical perspective |
| title_full | Statistical mechanics of disordered systems a mathematical perspective Anton Bovier ; Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin and Institut für Mathematik, Technsiche Universität Berlin |
| title_fullStr | Statistical mechanics of disordered systems a mathematical perspective Anton Bovier ; Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin and Institut für Mathematik, Technsiche Universität Berlin |
| title_full_unstemmed | Statistical mechanics of disordered systems a mathematical perspective Anton Bovier ; Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin and Institut für Mathematik, Technsiche Universität Berlin |
| title_short | Statistical mechanics of disordered systems |
| title_sort | statistical mechanics of disordered systems a mathematical perspective |
| title_sub | a mathematical perspective |
| topic | Statistical mechanics Mathematical statistics Probabilities System theory Mathematische Physik (DE-588)4037952-8 gnd Ungeordnetes System (DE-588)4124353-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Statistical mechanics Mathematical statistics Probabilities System theory Mathematische Physik Ungeordnetes System Statistische Mechanik |
| url | https://doi.org/10.1017/CBO9780511616808 |
| work_keys_str_mv | AT bovieranton statisticalmechanicsofdisorderedsystemsamathematicalperspective |