Canonical Gibbs Measures
Author : H. O. Georgii
Publisher : Springer
Page : 198 pages
File Size : 38,27 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540384847
Author : H. O. Georgii
Publisher : Springer
Page : 198 pages
File Size : 38,27 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540384847
Author : Hans-Otto Georgii
Publisher : Walter de Gruyter
Page : 561 pages
File Size : 47,80 MB
Release : 2011-05-31
Category : Mathematics
ISBN : 3110250322
"This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.
Author : Utkir A Rozikov
Publisher : World Scientific
Page : 367 pages
File Size : 15,11 MB
Release : 2022-07-28
Category : Mathematics
ISBN : 9811251258
This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.
Author : Barry Simon
Publisher : Princeton University Press
Page : 534 pages
File Size : 49,39 MB
Release : 2014-07-14
Category : Science
ISBN : 1400863430
A state-of-the-art survey of both classical and quantum lattice gas models, this two-volume work will cover the rigorous mathematical studies of such models as the Ising and Heisenberg, an area in which scientists have made enormous strides during the past twenty-five years. This first volume addresses, among many topics, the mathematical background on convexity and Choquet theory, and presents an exhaustive study of the pressure including the Onsager solution of the two-dimensional Ising model, a study of the general theory of states in classical and quantum spin systems, and a study of high and low temperature expansions. The second volume will deal with the Peierls construction, infrared bounds, Lee-Yang theorems, and correlation inequality. This comprehensive work will be a useful reference not only to scientists working in mathematical statistical mechanics but also to those in related disciplines such as probability theory, chemical physics, and quantum field theory. It can also serve as a textbook for advanced graduate students. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Sacha Friedli
Publisher : Cambridge University Press
Page : 643 pages
File Size : 16,43 MB
Release : 2017-11-23
Category : Mathematics
ISBN : 1107184827
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author : Anna DeMasi
Publisher : Springer
Page : 204 pages
File Size : 13,27 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540466363
Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.
Author : James Sethna
Publisher : OUP Oxford
Page : 374 pages
File Size : 12,93 MB
Release : 2006-04-07
Category : Science
ISBN : 0191566217
In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.
Author : Herbert Spohn
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 31,13 MB
Release : 2012-12-06
Category : Science
ISBN : 3642843719
This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the explanation of large-scale dynamics (evolution differential equations) from models of a very large number of interacting particles. This book addresses both researchers and students. Much of the material presented has never been published in book-form before.
Author : Dmitriĭ I︠A︡kovlevich Petrina
Publisher : Walter de Gruyter
Page : 310 pages
File Size : 46,82 MB
Release : 2009
Category : Hamiltonian systems
ISBN : 3110208040
The monograph is devoted to one of the most important trends in contemporary mathematical physics, the investigation of evolution equations of many-particle systems of statistical mechanics. The book systematizes rigorous results obtained in this field in recent years, and it presents contemporary methods for the investigation of evolution equations of infinite-particle systems. The book is intended for experts in statistical physics, mathematical physics, and probability theory and for students of universities specialized in mathematics and physics.
Author : Persi Diaconis
Publisher : Springer
Page : 460 pages
File Size : 16,23 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 354046042X
This volume contains detailed, worked-out notes of six main courses given at the Saint-Flour Summer Schools from 1985 to 1987.