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.
Author(s): A. J. Berlinsky, A. B. Harris
Publisher: Springer
Year: 2019
Language: English
Pages: 609
City: Switzerland AG
Front Matter ....Pages i-xxi
Front Matter ....Pages 1-1
Introduction (A. J. Berlinsky, A. B. Harris)....Pages 3-10
Phase Diagrams (A. J. Berlinsky, A. B. Harris)....Pages 11-25
Thermodynamic Properties and Relations (A. J. Berlinsky, A. B. Harris)....Pages 27-61
Front Matter ....Pages 63-63
Basic Principles (A. J. Berlinsky, A. B. Harris)....Pages 65-93
Examples (A. J. Berlinsky, A. B. Harris)....Pages 95-118
Basic Principles (Continued) (A. J. Berlinsky, A. B. Harris)....Pages 119-138
Noninteracting Gases (A. J. Berlinsky, A. B. Harris)....Pages 139-175
Front Matter ....Pages 177-177
Mean-Field Approximation for the Free Energy (A. J. Berlinsky, A. B. Harris)....Pages 179-200
Density Matrix Mean-Field Theory and Landau Expansions (A. J. Berlinsky, A. B. Harris)....Pages 201-222
Landau Theory for Two or More Order Parameters (A. J. Berlinsky, A. B. Harris)....Pages 223-261
Quantum Fluids (A. J. Berlinsky, A. B. Harris)....Pages 263-294
Superconductivity: Hartree–Fock for Fermions with Attractive Interactions (A. J. Berlinsky, A. B. Harris)....Pages 295-317
Qualitative Discussion of Fluctuations (A. J. Berlinsky, A. B. Harris)....Pages 319-344
The Cayley Tree (A. J. Berlinsky, A. B. Harris)....Pages 345-370
Front Matter ....Pages 371-371
Exact Mappings (A. J. Berlinsky, A. B. Harris)....Pages 373-403
Series Expansions (A. J. Berlinsky, A. B. Harris)....Pages 405-440
The Ising Model: Exact Solutions (A. J. Berlinsky, A. B. Harris)....Pages 441-476
Monte Carlo (A. J. Berlinsky, A. B. Harris)....Pages 477-493
Real Space Renormalization Group (A. J. Berlinsky, A. B. Harris)....Pages 495-519
The Epsilon Expansion (A. J. Berlinsky, A. B. Harris)....Pages 521-556
Kosterlitz-Thouless Physics (A. J. Berlinsky, A. B. Harris)....Pages 557-595
Back Matter ....Pages 597-602
