Thermodynamics of One-Dimensional Solvable Models

Exactly solvable models are very important in physics. They are important not just from a theoretical point of view but also from the experimentalist's perspective because in such cases theoretical results and experimental results can be compared without ambiguity. This 1999 book is 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 between 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. This book, written by one of the top physicists in this field, and the originator of much of the work in the subject, will be of great interest to theoretical condensed matter physicists.

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 delta-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 delta-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.

This 1999 book covers 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 crosses the boundaries between condensed matter physics, mathematics and field theory. The derivation and application of thermodynamic Bethe-ansatz equations for one-dimensional models are explained in detail.