Spin Glasses: A Challenge for Mathematicians

Spin Glasses: A Challenge for Mathematicians
Author: Michel Talagrand
Publisher: Springer Science & Business Media
Total Pages: 608
Release: 2003-07-11
Genre: Computers
ISBN: 9783540003564

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.

Spin Glasses and Complexity

Spin Glasses and Complexity
Author: Daniel L. Stein
Publisher: Princeton University Press
Total Pages: 336
Release: 2013-01-15
Genre: Science
ISBN: 1400845637

Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. Spin Glasses and Complexity offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity. This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into--and modify--this framework. It then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling. Providing an essential overview of the history, science, and growing significance of this exciting field, Spin Glasses and Complexity also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a must-have book for students and practitioners in the natural and social sciences, with new material even for the experts.

The Sherrington-Kirkpatrick Model

The Sherrington-Kirkpatrick Model
Author: Dmitry Panchenko
Publisher: Springer Science & Business Media
Total Pages: 164
Release: 2013-02-26
Genre: Mathematics
ISBN: 1461462894

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.

Mean Field Models for Spin Glasses

Mean Field Models for Spin Glasses
Author: Michel Talagrand
Publisher: Springer Science & Business Media
Total Pages: 633
Release: 2011-08-14
Genre: Mathematics
ISBN: 3642222536

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.

Spin Glasses and Random Fields

Spin Glasses and Random Fields
Author: A. Peter Young
Publisher: World Scientific
Total Pages: 454
Release: 1998
Genre: Science
ISBN: 9810232403

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.

Information, Physics, and Computation

Information, Physics, and Computation
Author: Marc Mézard
Publisher: Oxford University Press
Total Pages: 584
Release: 2009-01-22
Genre: Computers
ISBN: 019857083X

A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

Perspectives on Spin Glasses

Perspectives on Spin Glasses
Author: Pierluigi Contucci
Publisher: Cambridge University Press
Total Pages: 219
Release: 2013
Genre: Science
ISBN: 0521763347

Presenting and developing the theory of spin glasses for mathematical physicists and probabilists working in disordered systems.

Gaussian Processes on Trees

Gaussian Processes on Trees
Author: Anton Bovier
Publisher: Cambridge University Press
Total Pages: 211
Release: 2017
Genre: Mathematics
ISBN: 1107160499

This book presents recent advances in branching Brownian motion from the perspective of extreme value theory and statistical physics, for graduates.

Combinatorial Stochastic Processes

Combinatorial Stochastic Processes
Author: Jim Pitman
Publisher: Springer Science & Business Media
Total Pages: 257
Release: 2006-05-11
Genre: Mathematics
ISBN: 354030990X

The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

Mathematicians of the World, Unite!

Mathematicians of the World, Unite!
Author: Guillermo Curbera
Publisher: CRC Press
Total Pages: 336
Release: 2009-02-23
Genre: Mathematics
ISBN: 1439865124

This vividly illustrated history of the International Congress of Mathematicians- a meeting of mathematicians from around the world held roughly every four years- acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century. Because the congress is an int