Mathematical Statistical Physics
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Author | : Robert Adolʹfovich Minlos |
Publisher | : American Mathematical Soc. |
Total Pages | : 114 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821813374 |
Download Introduction to Mathematical Statistical Physics Book in PDF, Epub and Kindle
This book presents a mathematically rigorous approach to the main ideas and phenomena of statistical physics. The introduction addresses the physical motivation, focusing on the basic concept of modern statistical physics, that is the notion of Gibbsian random fields. Properties of Gibbsian fields are analysed in two ranges of physical parameters: "regular" (corresponding to high-temperature and low-density regimes) where no phase transition is exhibited, and "singular" (low temperature regimes) where such transitions occur. Next, a detailed approach to the analysis of the phenomena of phase transitions of the first kind, the Pirogov-Sinai theory, is presented. The author discusses this theory in a general way and illustrates it with the example of a lattice gas with three types of particles. The conclusion gives a brief review of recent developments arising from this theory. The volume is written for the beginner, yet advanced students will benefit from it as well. The book will serve nicely as a supplementary textbook for course study. The prerequisites are an elementary knowledge of mechanics, probability theory and functional analysis.
Author | : Colin J. Thompson |
Publisher | : Princeton University Press |
Total Pages | : 289 |
Release | : 2015-03-08 |
Genre | : Science |
ISBN | : 1400868688 |
Download Mathematical Statistical Mechanics Book in PDF, Epub and Kindle
While most introductions to statistical mechanics are either too mathematical or too physical, Colin Thompson's book combines mathematical rigor with familiar physical materials. Following introductory chapters on kinetic theory, thermodynamics, the Gibbs ensembles, and the thermodynamic limit, later chapters discuss the classical theories of phase transitions, the Ising model, algebraic methods and combinatorial methods for solving the two-dimensional model in zero field, and some applications of the Ising model to biology. Originally published in 1979. 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 |
Total Pages | : 643 |
Release | : 2017-11-23 |
Genre | : Mathematics |
ISBN | : 1107184827 |
Download Statistical Mechanics of Lattice Systems Book in PDF, Epub and Kindle
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author | : Aleksandr I?Akovlevich Khinchin |
Publisher | : Courier Corporation |
Total Pages | : 212 |
Release | : 1949-01-01 |
Genre | : Mathematics |
ISBN | : 9780486601472 |
Download Mathematical Foundations of Statistical Mechanics Book in PDF, Epub and Kindle
Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.
Author | : Martin Loebl |
Publisher | : Springer Science & Business Media |
Total Pages | : 187 |
Release | : 2010-02-16 |
Genre | : Science |
ISBN | : 3834893293 |
Download Discrete Mathematics in Statistical Physics Book in PDF, Epub and Kindle
The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently. It also naturally leads to many open problems, some of which seem to be basic. Hopefully, this book will help making these exciting problems attractive to advanced students and researchers.
Author | : Marek Biskup |
Publisher | : Springer Science & Business Media |
Total Pages | : 356 |
Release | : 2009-03-25 |
Genre | : Mathematics |
ISBN | : 3540927956 |
Download Methods of Contemporary Mathematical Statistical Physics Book in PDF, Epub and Kindle
This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. An introductory chapter on lattice spin models is useful as a background for other lectures of the collection. The topics include new results on phase transitions for gradient lattice models (with introduction to the techniques of the reflection positivity), stochastic geometry reformulation of classical and quantum Ising models, the localization/delocalization transition for directed polymers. A general rigorous framework for theory of metastability is presented and particular applications in the context of Glauber and Kawasaki dynamics of lattice models are discussed. A pedagogical account of several recently discussed topics in nonequilibrium statistical mechanics with an emphasis on general principles is followed by a discussion of kinetically constrained spin models that are reflecting important peculiar features of glassy dynamics.
Author | : Richard Chace Tolman |
Publisher | : Courier Corporation |
Total Pages | : 700 |
Release | : 1979-01-01 |
Genre | : Science |
ISBN | : 9780486638966 |
Download The Principles of Statistical Mechanics Book in PDF, Epub and Kindle
This is the definitive treatise on the fundamentals of statistical mechanics. A concise exposition of classical statistical mechanics is followed by a thorough elucidation of quantum statistical mechanics: postulates, theorems, statistical ensembles, changes in quantum mechanical systems with time, and more. The final two chapters discuss applications of statistical mechanics to thermodynamic behavior. 1930 edition.
Author | : Aleksandr I?Akovlevich Khinchin |
Publisher | : Courier Corporation |
Total Pages | : 210 |
Release | : 1949-01-01 |
Genre | : Mathematics |
ISBN | : 0486601471 |
Download Mathematical Foundations of Statistical Mechanics Book in PDF, Epub and Kindle
Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.
Author | : Johannes Voit |
Publisher | : Springer Science & Business Media |
Total Pages | : 227 |
Release | : 2013-06-29 |
Genre | : Science |
ISBN | : 3662044234 |
Download The Statistical Mechanics of Financial Markets Book in PDF, Epub and Kindle
A careful examination of the interaction between physics and finance. It takes a look at the 100-year-long history of co-operation between the two fields and goes on to provide new research results on capital markets - taken from the field of statistical physics. The random walk model, well known in physics, is one good example of where the two disciplines meet. In the world of finance it is the basic model upon which the Black-Scholes theory of option pricing and hedging has been built. The underlying assumptions are discussed using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion. On this basis, new theories of derivative pricing and risk control can be formulated.
Author | : |
Publisher | : Elsevier |
Total Pages | : 849 |
Release | : 2006-06-27 |
Genre | : Science |
ISBN | : 0080479235 |
Download Mathematical Statistical Physics Book in PDF, Epub and Kindle
The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians. Introduction to a field of math with many interdisciplinary connections in physics, biology, and computer science Roadmap to the next decade of mathematical statistical mechanics Volume for reference years to come