Book contents
- Frontmatter
- Contents
- Foreword
- Translator's note
- Introduction
- 1 The chain of spin-1/2 atoms
- 2 Thermodynamic limit of the Heisenberg–Ising chain
- 3 Thermodynamics of the spin-1/2 chain: Limiting cases
- 4 δ-Interacting bosons
- 5 Bethe wavefunctions associated with a reflection group
- 6 Continuum limit of the spin chain
- 7 The six-vertex model
- 8 The eight-vertex model
- 9 The eight-vertex model: Eigenvectors and thermodynamics
- 10 Identical particles with δ-interactions
- 11 Identical particles with δ-interactions: General solution for two internal states
- 12 Identical particles with δ-interactions: General solution for n components and limiting cases
- 13 Various corollaries and extensions
- 14 On the Toda chain
- References
- Index
Introduction
Published online by Cambridge University Press: 05 April 2014
- Frontmatter
- Contents
- Foreword
- Translator's note
- Introduction
- 1 The chain of spin-1/2 atoms
- 2 Thermodynamic limit of the Heisenberg–Ising chain
- 3 Thermodynamics of the spin-1/2 chain: Limiting cases
- 4 δ-Interacting bosons
- 5 Bethe wavefunctions associated with a reflection group
- 6 Continuum limit of the spin chain
- 7 The six-vertex model
- 8 The eight-vertex model
- 9 The eight-vertex model: Eigenvectors and thermodynamics
- 10 Identical particles with δ-interactions
- 11 Identical particles with δ-interactions: General solution for two internal states
- 12 Identical particles with δ-interactions: General solution for n components and limiting cases
- 13 Various corollaries and extensions
- 14 On the Toda chain
- References
- Index
Summary
From the exact solution of the Ising model by Onsager in 1944 up to that of the hard hexagon model by Baxter in 1980, the statistical mechanics of two-dimensional systems has been enriched by a number of exact results. One speaks (in quick manner) of exact models once a convenient mathematical expression has been obtained for a physical quantity such as the free energy, an order parameter or some correlation, or at the very least once their evaluation is reduced to a problem of classical analysis. Such solutions, often considered as singular curiosities upon their appearance, often have the interest of illustrating the principles and general theorems rigorously established in the framework of definitive theories, and also enabling the control of approximate or perturbative methods applicable to more realistic and complex models. In the theory of phase transitions, the Ising model and the results of Onsager and Yang have eminently played such a reference role. With the various vertex models, the methods of Lieb and Baxter have extended this role and the collection of critical exponents, providing new useful elements of comparison with extrapolation methods, and forcing a refinement of the notion of universality. Intimately linked to two-dimensional classical models (but of less interest for critical phenomena), one-dimensional quantum models such as the linear magnetic chain and Bethe's famous solution have certainly contributed to the understanding of fundamental excitations in many-body systems. One could also mention the physics of one-dimensional conductors.
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- The Bethe Wavefunction , pp. xii - xviPublisher: Cambridge University PressPrint publication year: 2014