STATISTICAL MECHANICS MADE SIMPLE: A GUIDE FOR STUDENTS AND RESEARCHERS - Hardcover

Mattis, Daniel C.

Hardcover

ISBN 10: 9812381651 ISBN 13: 9789812381651

Publisher: World Scientific Pub Co Inc, 2003

Synopsis

This book is an elaboration of the author's lecture notes in a graduate course in statistical physics and thermodynamics, augmented by some material suitable for self-teaching as well as for undergraduate study. The first 4 or 5 chapters are suitable for an undergraduate course for engineers and physicists in Thermodynamics and Statistical Physics and include detailed study of the various ensembles and their connections to applied thermodynamics. The Debye law of specific heats and reasons for deviations from the Debye formulas are covered, as are the Einstein theories of Brownian motion, black-body radiation and specific heat of solids. Van der Waals gases and the reason for the apparent failure of his Law of Corresponding States are discussed.

The last 5 chapters treat topics of recent interest to researchers, including: the Ising and Potts models, spin waves in ferromagnetic and anti-ferromagnetic media, sound propagation in non-ideal gases and the decay of sound waves, introduction to the understanding of glasses and spin glasses, superfluidity and superconductivity.

The selection of material is wide-ranging and the mathematics for handling it completely self-contained, ranging from counting (probability theory) to quantum field theory as used in the study of fermions, bosons and as an adjunct in the solutions of the equations of classical diffusion-reaction theory. In addition to the standard material found in most recent books on statistical physics the constellation of topics covered in this text includes numerous original items:

· Generalization of "negative temperature" to interacting spins
· Derivation of Gibbs' factor from first principles
· Exact free energy of interacting particles in 1D (e.g., classical and quantum Tonk's gas)
· Introduction to virial expansions, Equations of State, Correlation Functions and "critical exponents"
· Superfluidity in ideal and non-ideal fluids (both Bogolubov and Feynman theories)
· Superconductivity: thermodynamical approach and the BCS theory
· Derivation of "Central Limit Theorem" and its applications
· Boltzmann's "H-Theorem" and the nonlinear Boltzmann equation
· Exact solution of nonlinear Boltzmann Equation for electrons in time-dependent electric field and the derivation of Joule heating, transport parameters in crossed electric and magnetic fields, etc.
· Frequency spectrum and decay of sound waves in gases
· Exact evaluation of free energy and thermodynamic properties of the two-dimensional Ising model in regular and fully frustrated (spin-glass like) lattices
· The "zipper" model of crystal fracture or polymer coagulation - calculation of Tc
· Potts model in 2D: duality and Tc
· "Doi's theory" of diffusion-limited chemical reactions with some exact results — including the evaluation of statistical fluctuations in radioactive decay
· Thermodynamic Green Functions and their applications to fermions and bosons with an example drawn from random matrix theory

and much more.

About this title

From the Publisher

Readership: Upper level undergraduates, graduate students, academics and researchers in statistical physics.

Review

...this book gives insight into and connections of various physical facts and phenomena.. -- ACTA Physica Slovaca, Oct 2003

A valuable addition to any statistical physicist's library. -- American Journal of Physics

An admirable piece of work by an outstanding expert in the field. -- Physics Today

The book can enthusiastically be recommended either as main text or as companion text for a one-semester course -- Professor Elliot Lieb, Princeton University, USA

a good choice for those considering becoming theorists as it gives many examples -- Canadian Undergraduate Physics Journal, Apr 2003

the author's expertise and enthusiasm for this area are apparent -- Journal of Statistical Physics, Feb 2004

... a rather original contribution to the statistical mechanical literature. -- Mathematical Reviews

Edition details

• Publisher: World Scientific Pub Co Inc
• Publication date: 2003
• Language: English
• ISBN 10: 9812381651
• ISBN 13: 9789812381651
• Binding: Hardcover
• Number of pages: 268