Topics in Disordered Systems
Author | : Charles M Newman |
Publisher | : |
Total Pages | : 100 |
Release | : 1997-09-23 |
Genre | : |
ISBN | : 9783034889131 |
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Author | : Charles M Newman |
Publisher | : |
Total Pages | : 100 |
Release | : 1997-09-23 |
Genre | : |
ISBN | : 9783034889131 |
Author | : Charles M. Newman |
Publisher | : Birkhäuser |
Total Pages | : 93 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034889127 |
Disordered systems are statistical mechanics models in random environments. This lecture notes volume concerns the equilibrium properties of a few carefully chosen examples of disordered Ising models. The approach is that of probability theory and mathematical physics, but the subject matter is of interest also to condensed matter physicists, material scientists, applied mathematicians and theoretical computer scientists. (The two main types of systems considered are disordered ferromagnets and spin glasses. The emphasis is on questions concerning the number of ground states (at zero temperature) or the number of pure Gibbs states (at nonzero temperature). A recurring theme is that these questions are connected to interesting issues concerning percolation and related models of geometric/combinatorial probability. One question treated at length concerns the low temperature behavior of short-range spin glasses: whether and in what sense Parisi's analysis of the meanfield (or "infinite-range") model is relevant. Closely related is the more general conceptual issue of how to approach the thermodynamic (i.e., infinite volume) limit in systems which may have many complex competing states. This issue has been addressed in recent joint work by the author and Dan Stein and the book provides a mathematically coherent presentation of their approach.)
Author | : Charles M. Newman |
Publisher | : Springer Science & Business Media |
Total Pages | : 100 |
Release | : 1997-09-23 |
Genre | : Mathematics |
ISBN | : 9783764357771 |
Disordered systems are statistical mechanics models in random environments. This lecture notes volume concerns the equilibrium properties of a few carefully chosen examples of disordered Ising models. The approach is that of probability theory and mathematical physics, but the subject matter is of interest also to condensed matter physicists, material scientists, applied mathematicians and theoretical computer scientists. (The two main types of systems considered are disordered ferromagnets and spin glasses. The emphasis is on questions concerning the number of ground states (at zero temperature) or the number of pure Gibbs states (at nonzero temperature). A recurring theme is that these questions are connected to interesting issues concerning percolation and related models of geometric/combinatorial probability. One question treated at length concerns the low temperature behavior of short-range spin glasses: whether and in what sense Parisi's analysis of the meanfield (or "infinite-range") model is relevant. Closely related is the more general conceptual issue of how to approach the thermodynamic (i.e., infinite volume) limit in systems which may have many complex competing states. This issue has been addressed in recent joint work by the author and Dan Stein and the book provides a mathematically coherent presentation of their approach.)
Author | : Pierluigi Contucci |
Publisher | : |
Total Pages | : |
Release | : 2017 |
Genre | : SCIENCE |
ISBN | : 9781316869048 |
Author | : Gautam I Menon |
Publisher | : Springer |
Total Pages | : 185 |
Release | : 2012-03-15 |
Genre | : Science |
ISBN | : 9386279517 |
Disordered systems are ubiquitous in nature and their study remains a profound and challenging subject of current research. Ideas and methods from the physics of Disordered systems have been fruitfully applied to several fields ranging from computer science to neuroscience. This book contains a selection of lectures delivered at the 'SERC School on Disordered Systems', spanning topics from classic results to frontier areas of research in this field. Spin glasses, disordered Ising models, quantum disordered systems, structural glasses, dilute magnets, interfaces in random field systems and disordered vortex systems are among the topics discussed in the text, in chapters authored by active researchers in the field, including Bikas Chakrabarti, Arnab Das, Deepak Kumar, Gautam Menon, G. Ravikumar, Purusattam Ray, Srikanth Sastry and Prabodh Shukla. This book provides a gentle and comprehensive introduction to the physics of disordered systems and is aimed at graduate students and young scientists either working in or intending to enter this exciting field. It should also serve as a general reference for students and practicing researchers alike.
Author | : Günter Radons |
Publisher | : Springer Science & Business Media |
Total Pages | : 377 |
Release | : 2005-11-02 |
Genre | : Science |
ISBN | : 3540268693 |
Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.
Author | : Daniel Alpay |
Publisher | : Birkhäuser |
Total Pages | : 420 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034882157 |
This volume is dedicated to Harry Dym, a leading expert in operator theory, on the occasion of his sixtieth birthday. The book opens with an autobiographical sketch, a list of publications and a personal account of I. Gohberg on his collaboration with Harry Dym. The mathematical papers cover Krein space operator theory, Schur analysis and interpolation, several complex variables and Riemann surfaces, matrix theory, system theory, and differential equations and mathematical physics. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Author | : Alejandro Ramirez |
Publisher | : |
Total Pages | : 184 |
Release | : 2014-07-31 |
Genre | : |
ISBN | : 9781493903405 |
Author | : Véronique Gayrard |
Publisher | : Springer Nature |
Total Pages | : 279 |
Release | : 2019-09-15 |
Genre | : Mathematics |
ISBN | : 3030290778 |
These proceedings of the conference Advances in Statistical Mechanics, held in Marseille, France, August 2018, focus on fundamental issues of equilibrium and non-equilibrium dynamics for classical mechanical systems, as well as on open problems in statistical mechanics related to probability, mathematical physics, computer science, and biology. Statistical mechanics, as envisioned more than a century ago by Boltzmann, Maxwell and Gibbs, has recently undergone stunning twists and developments which have turned this old discipline into one of the most active areas of truly interdisciplinary and cutting-edge research. The contributions to this volume, with their rather unique blend of rigorous mathematics and applications, outline the state-of-the-art of this success story in key subject areas of equilibrium and non-equilibrium classical and quantum statistical mechanics of both disordered and non-disordered systems. Aimed at researchers in the broad field of applied modern probability theory, this book, and in particular the review articles, will also be of interest to graduate students looking for a gentle introduction to active topics of current research.