Statistical Mechanics

In a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph.D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects.

The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson's epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods due to Anderson, Kosterlitz, Thouless and Young.

Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.

Written by experienced instructors who have class tested materials in the book over a period of years Offers many examples and exercises to test student understanding Includes novel and interesting topics for independent study and projects

Auteur

John Berlinsky received his PhD from the University of Pennsylvania in 1972. He was a post-doc at the University of British Columbia (UBC) and the University of Amsterdam before joining the faculty of UBC in 1977. In 1986 he moved to McMaster University where he is now Emeritus Professor of Physics. He also served as Academic Program Director and as Founding Director of Perimeter Scholars International at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, from 2008-2014 and as Associate Director of the Kavli Institute for Theoretical Physics in Santa Barbara, California from 2014-2016. John was an Alfred P. Sloan Foundation Fellow and he is a Fellow of the American Physical Sollciety.

Brooks Harris received his PhD from Harvard in 1962. He was a post-doc at Duke University and at the Atomic Energy Research Establishment at Harwell in the UK. He joined the faculty of the University of Pennsylvania in 1962, where he is now Professor of Physics Emeritus. Brooks was an Alfred P. Sloan and John Simon Guggenheim Fellow and, he is a Fellow of the American Physical Society. In 2007, he was awarded the Lars Onsager Prize of the American Physical Society, "For his many contributions to the statistical physics of random systems, including the formulation of the Harris criterion, which has led to numerous insights into a variety of disordered systems."

Contenu
I Preliminaries .- Introduction.- Phase Diagrams.- Thermodynamic Properties and Relations.- II Basic Formalism .- Basic Principles.- Examples.- Basic Principles (Continued).- Noninteracting Gases.- III Mean Field Theory, Landau Theory .- Mean-Field Approximation for the Free Energy.- Density Matrix Mean-Field Theory and Landau Expansions.- Landau Theory for Two or More Order Parameters.- Quantum Fluids.- Theory of Superconductivity.- Qualitative Discussion of Fluctuations.- The Cayley Tree.- IV Beyond Mean Field Theory .- Exact Mappings.- Series Expansions.- The Ising Model: Exact Solutions.- Monte Carlo.- Real Space Renormalization Group.- The Epsilon Expansion.- Kosterlitz-Thouless Physics.