Buch, Englisch, Band 55, 632 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1121 g
Volume II: Advanced Replica-Symmetry and Low Temperature
Buch, Englisch, Band 55, 632 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1121 g
ISBN: 978-3-642-22252-8
Verlag: Springer
This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
- Naturwissenschaften Physik Quantenphysik
Weitere Infos & Material
Part I. Advanced Replica-Symmetry. - The Gardener Formula for the sphere. - The Gardener Formula for the Discrete Cube. - The Hopfield Model. - The SK Model Without External Field. - Part II. Low Temperature. - The Ghirlanda-Guerra Identities. - The High-Temperature Region of the SK Model. - The Parisi Formula. - The Parisi Solution. - The p-spin Interaction Model. - Appendix: Elements of Probability Theory. - References. - Index.
