The Sherrington Kirkpatrick Model
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Author | : Dmitry Panchenko |
Publisher | : Springer Science & Business Media |
Total Pages | : 164 |
Release | : 2013-02-26 |
Genre | : Mathematics |
ISBN | : 1461462894 |
Download The Sherrington-Kirkpatrick Model Book in PDF, Epub and Kindle
The 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.
Author | : |
Publisher | : Springer |
Total Pages | : 170 |
Release | : 2013-02-22 |
Genre | : |
ISBN | : 9781461462903 |
Download The Sherrington-Kirkpatrick Model Book in PDF, Epub and Kindle
Author | : Philipp Thomann |
Publisher | : |
Total Pages | : 151 |
Release | : 2012 |
Genre | : |
ISBN | : |
Download A Generalization of the Sherrington-Kirkpatrick Model Book in PDF, Epub and Kindle
Author | : Michel Talagrand |
Publisher | : Springer Science & Business Media |
Total Pages | : 608 |
Release | : 2003-07-11 |
Genre | : Computers |
ISBN | : 9783540003564 |
Download Spin Glasses: A Challenge for Mathematicians Book in PDF, Epub and Kindle
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, that physicists studied by non-rigorous methods. They predicted spectacular behaviors, previously unknown in probability theory. They believe these behaviors occur in many models of considerable interest for several branches of science (statistical physics, neural networks and computer science). This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics, and contains proofs in complete detail of much of what is rigorously known on spin glasses at the time of writing.
Author | : Cirano De Dominicis |
Publisher | : Cambridge University Press |
Total Pages | : 240 |
Release | : 2006-10-26 |
Genre | : Science |
ISBN | : 9780521847834 |
Download Random Fields and Spin Glasses Book in PDF, Epub and Kindle
The book introduces some useful and little known techniques in statistical mechanics and field theory including multiple Legendre transforms, supersymmetry, Fourier transforms on a tree, infinitesimal permutations and Ward Takahashi Identities."--Jacket.
Author | : N. Parga |
Publisher | : |
Total Pages | : 21 |
Release | : 1985 |
Genre | : |
ISBN | : |
Download On the Locally Stable States of the Sherrington-Kirkpatrick Model Book in PDF, Epub and Kindle
Author | : Marc Mezard |
Publisher | : World Scientific Publishing Company |
Total Pages | : 477 |
Release | : 1987-11-01 |
Genre | : Science |
ISBN | : 9813103914 |
Download Spin Glass Theory And Beyond: An Introduction To The Replica Method And Its Applications Book in PDF, Epub and Kindle
This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular attention to new applications in the study of optimization theory and neural networks. About two-thirds of the book are a collection of the most interesting and pedagogical articles on the subject.
Author | : Henry P. McKean |
Publisher | : American Mathematical Society |
Total Pages | : 159 |
Release | : 2024-05-23 |
Genre | : Mathematics |
ISBN | : 1470477874 |
Download Stochastic Integrals Book in PDF, Epub and Kindle
This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. —E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplementary reading or independent study. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications.
Author | : Michel Talagrand |
Publisher | : |
Total Pages | : 504 |
Release | : 2011 |
Genre | : Spin glasses |
ISBN | : 9783642152030 |
Download Mean Field Models for Spin Glasses Book in PDF, Epub and Kindle
Author | : A. Peter Young |
Publisher | : World Scientific |
Total Pages | : 454 |
Release | : 1998 |
Genre | : Science |
ISBN | : 9810232403 |
Download Spin Glasses and Random Fields Book in PDF, Epub and Kindle
The last few years have seen many developments in the study of ?frustrated? systems, such as spin glasses and random fields. In addition, the application of the idea of spin glasses to other branches of physics, such as vortex lines in high temperature superconductors, protein folding, structural glasses, and the vulcanization of rubber, has been flourishing. The earlier reviews are several years old, so now is an appropriate time to summarize the recent developments. The articles in this book have been written by leading researchers and include theoretical and experimental studies, and large-scale numerical work (using state-of-the-art algorithms designed specifically for spin-glass-type problems), as well as analytical studies.