Canonical Gibbs Measures
Author: H. O. Georgii
Publisher:
Published: 2014-01-15
Total Pages: 204
ISBN-13: 9783662175255
DOWNLOAD EBOOK →Author: H. O. Georgii
Publisher:
Published: 2014-01-15
Total Pages: 204
ISBN-13: 9783662175255
DOWNLOAD EBOOK →Author: H. O. Georgii
Publisher: Springer
Published: 2006-11-15
Total Pages: 198
ISBN-13: 3540384847
DOWNLOAD EBOOK →Author: Younghak Kwon
Publisher:
Published: 2021
Total Pages: 240
ISBN-13:
DOWNLOAD EBOOK →We consider a one-dimensional lattice system of unbounded, real-valued spins with arbitrarystrong, quadratic, finite-range interaction. The first area of interest concerns the equivalence of the grand canonical ensemble and the canonical ensemble: on the level of thermodynamic functions, on the level of observables, and on the level of correlations. More precisely, in the thermodynamic limit (size N of the system goes to infinity), we show that the free energy, expectation of intensive observable, and correlation of two intensive functions are the same for the grand canonical ensemble and canonical ensemble. The second area of interest concerns the decay of correlations and uniqueness of infinite-volume Gibbs measure of the canonical ensemble. It is shown that the correlations of the canonical ensemble decay exponentially plus a volume correction term. As a consequence, we verify a conjecture that the infinite-volume Gibbs measure of the canonical ensemble is unique on the one-dimensional lattice, extending results that are known for the case of weak interaction. The third area of interest concerns the logarithmic Sobolev inequality (LSI). It is shown that the canonical ensemble satisfies a uniform LSI. The LSI constant is uniform in the boundary data, the external field and scales optimally in the system size. We deduce the LSI by combining two different methods, the two-scale approach and the Zegarlinski method. The last area of interest concerns the hydrodynamic limit. We deduce the hydrodynamic limit of Kawasaki dynamics. The main ingredients are uniform LSI and decay of correlations for the canonical ensemble. The proof is based on a method invented by Grunewald, Otto, Villani and Westdickenberg.
Author: Hans-Otto Georgii
Publisher: Walter de Gruyter
Published: 2011-05-31
Total Pages: 561
ISBN-13: 3110250322
DOWNLOAD EBOOK →"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: Antonino Mazzeo
Publisher: Springer
Published: 2008-07-08
Total Pages: 0
ISBN-13: 9780387097121
DOWNLOAD EBOOK →This book constitutes the refereed proceedings of Industry Oriented Conferences held at IFIP 20th World Computer Congress in September 2008. The IFIP series publishes state-of-the-art results in the sciences and technologies of information and communication. The scope of the series includes: foundations of computer science; software theory and practice; education; computer applications in technology; communication systems; systems modeling and optimization; information systems; computers and society; computer systems technology; security and protection in information processing systems; artificial intelligence; and human-computer interaction. Proceedings and post-proceedings of refereed international conferences in computer science and interdisciplinary fields are featured. These results often precede journal publication and represent the most current research. The principal aim of the IFIP series is to encourage education and the dissemination and exchange of information about all aspects of computing.
Author: Utkir A. Rozikov
Publisher: World Scientific
Published: 2013
Total Pages: 404
ISBN-13: 9814513385
DOWNLOAD EBOOK →The Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Moreover, the Gibbs measure is the unique measure that maximizes the entropy for a given expected energy. The method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees, and nonlinear analysis. This book discusses all the mentioned methods, which were developed recently.
Author: Antonino Mazzeo
Publisher: Springer
Published: 2008-07-08
Total Pages: 308
ISBN-13: 9780387097121
DOWNLOAD EBOOK →This book constitutes the refereed proceedings of Industry Oriented Conferences held at IFIP 20th World Computer Congress in September 2008. The IFIP series publishes state-of-the-art results in the sciences and technologies of information and communication. The scope of the series includes: foundations of computer science; software theory and practice; education; computer applications in technology; communication systems; systems modeling and optimization; information systems; computers and society; computer systems technology; security and protection in information processing systems; artificial intelligence; and human-computer interaction. Proceedings and post-proceedings of refereed international conferences in computer science and interdisciplinary fields are featured. These results often precede journal publication and represent the most current research. The principal aim of the IFIP series is to encourage education and the dissemination and exchange of information about all aspects of computing.
Author: Hans-Otto Georgii
Publisher: Walter de Gruyter
Published: 2011
Total Pages: 561
ISBN-13: 3110250292
DOWNLOAD EBOOK →From a review of the first edition: "This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] 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." (F. Papangelou