Statistical mechanics of lattice systems : a concrete mathematical introduction / S. Friedli, Y. Velenik.

Format:

Book

Author/Creator:

Friedli, Sacha, 1974- author.

Velenik, Yvan, 1970- author.

Series:

Cambridge books online.

Language:

English

Subjects (All):

Statistical mechanics.

Physical Description:

1 online resource (xix, 622 pages) : digital, PDF file(s)

Place of Publication:

Cambridge : Cambridge University Press, 2018.

System Details:

text file

PDF

Summary:

This motivating textbook gives a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie-Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kać interactions. Using classical concepts such as Gibbs measures, pressure, free energy, and entropy, the book exposes the main features of the classical description of large systems in equilibrium, in particular the central problem of phase transitions. It treats such important topics as the Peierls argument, the Dobrushin uniqueness, Mermin-Wagner and Lee-Yang theorems, and develops from scratch such workhorses as correlation inequalities, the cluster expansion, Pirogov-Sinai Theory, and reflection positivity. Written as a self-contained course for advanced undergraduate or beginning graduate students, the detailed explanations, large collection of exercises (with solutions), and appendix of mathematical results and concepts also make it a handy reference for researchers in related areas.

Contents:

The Curie-Weiss model

The Ising model

Liquid-vapor equilibrium

Cluster expansion

Infinite-volume Gibbs measures

Pirogov-Sinai theory

The Gaussian free field on Zd

Models with continuous symmetry

Reflection positivity.

Notes:

Title from publisher's bibliographic system (viewed on 17 Nov 2017).

Other Format:

Print version:

ISBN:

9781316882603

Access Restriction:

Restricted for use by site license.