# Statistical Mechanics

## An Introductory Graduate Course

Part of the Graduate Texts in Physics book series (GTP)

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Part of the Graduate Texts in Physics book series (GTP)

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.

Wilson’s epsilon expansion renormalization group formalism Monte Carlo methods density matrix formalism quenched randomness mean field theory order parameters Landau Expansion Bose and Fermi Gases

- DOI https://doi.org/10.1007/978-3-030-28187-8
- Copyright Information Springer Nature Switzerland AG 2019
- Publisher Name Springer, Cham
- eBook Packages Physics and Astronomy
- Print ISBN 978-3-030-28186-1
- Online ISBN 978-3-030-28187-8
- Series Print ISSN 1868-4513
- Series Online ISSN 1868-4521
- Buy this book on publisher's site