Thermodynamics of One-Dimensional Solvable Models

by Minoru Takahashi

Overview

Exactly solvable models are very important in physics from a theoretical point of view and also from the experimentalist's perspective, because in such cases theoretical results and experimental results can be compared without ambiguity. This is a book about an important class of exactly solvable models in physics. The subject area is the Bethe-ansatz approach for a number of one-dimensional models, and the setting up of equations within this approach to determine the thermodynamics of these systems. It is a topic that crosses the boundaries among condensed matter physics, mathematics and field theory. The derivation and application of thermodynamic Bethe-ansatz equations for one-dimensional models are explained in detail. This technique is indispensable for physicists studying the low-temperature properties of one-dimensional substances. Written by the originator of much of the work in the subject, this book will be of great interest to theoretical condensed matter physicists.

Product Details

ISBN-13:	9780521019798
Publisher:	Cambridge University Press
Publication date:	09/15/2005
Edition description:	Revised ed.
Pages:	268
Product dimensions:	6.69(w) x 9.65(h) x 0.55(d)

Table of Contents

Part I. Thermodynamics of Non-Interacting Systems and Ground States on Interacting Systems: 1. Free energy and correlation functions of XY models; 2. Systems with Δ-function potential; 3. Isotropic Heisenberg model; 4. XXZ model; 5. XYZ and eight-vertex models; 6. Hubbard model; Part II. Finite Temperature Integral Equations for Un-Nested Systems: 7. Repulsive Δ-function bosons; 8. Thermodynamics of the XXX chain; 9. Thermodynamics of the XXZ model; 10. Thermodynamics of the XYZ model; 11. Low-temperature thermodynamics; Part III. Finite Temperature Integral Equations for Nested Systems: 12. S=1/2 fermions with repulsive potential in the continuum; 13. S=1/2 fermions with an attractive potential; 14. Thermodynamics of the Hubbard model; Part IV. Quantum Transfer Matrix and Recent Developments: 15. Transfer matrix and correlation length; 16. The spin 1/2 XXZ model in a magnetic field; 17. The XYZ model with no magnetic field; 18. Recent developments and related topics.

Editorial Reviews

'Ever since Lars Onsager produced his celebrated solution of the two-dimensional Ising model, physicists have been persuaded of the pivotal role played by exactly solved models in statistical mechanics. Takahashi is a recognized expert in this field and his book summarizes what is known.' R. Evans, Contemporary Physics

'The book may be useful for mathematicians interested in spectral analysis and quite important for experts in quantum statistical mechanics.' Zentralblatt MATH

From the Publisher