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Algebraic Analysis of Solvable Lattice Models

Michio Jimbo Kyoto University, Kyoto, Japan
Tetsuji Miwa Kyoto University, Kyoto, Japan
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-0320-2
Product Code: CBMS/85
List Price: $27.00 Individual Price:$21.60
Electronic ISBN: 978-1-4704-2445-9
Product Code: CBMS/85.E
List Price: $25.00 Individual Price:$20.00
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List Price: $40.50 Click above image for expanded view Algebraic Analysis of Solvable Lattice Models Michio Jimbo Kyoto University, Kyoto, Japan Tetsuji Miwa Kyoto University, Kyoto, Japan A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-0-8218-0320-2 Product Code: CBMS/85  List Price:$27.00 Individual Price: $21.60  Electronic ISBN: 978-1-4704-2445-9 Product Code: CBMS/85.E  List Price:$25.00 Individual Price: $20.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$40.50
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 851995; 152 pp
MSC: Primary 17; 81; 82;

Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin $1/2$ XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the $XXX$ model is briefly discussed, and the book closes with a discussion of other types of models and related works.

• Chapters
• 0. Background of the problem
• 1. The spin $1/2$ XXZ model for $\Delta < - 1$
• 2. The six-vertex model in the anti-ferroelectric regime
• 3. Solvability and Symmetry
• 4. Correlation functions—physical derivation
• 5. Level one modules and bosonization
• 6. Vertex operators
• 7. Space of states—mathematical picture
• 8. Traces of vertex operators
• 9. Correlation functions and form factors
• 10. The $XXX \lim {q \to 1}$
• 11. Discussions
• 13. A. List of formulas
• Reviews

• The book provides a very clear exposition on the subject, and meanwhile gives an elementary introduction to representation theory … serves very well as both introduction and reference.

Mathematical Reviews
• Very clearly written … suitable for those who may not be expert either in quantum groups or in the theory of solvable lattice models.

Zentralblatt MATH
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 851995; 152 pp
MSC: Primary 17; 81; 82;

Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin $1/2$ XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the $XXX$ model is briefly discussed, and the book closes with a discussion of other types of models and related works.

• Chapters
• 0. Background of the problem
• 1. The spin $1/2$ XXZ model for $\Delta < - 1$
• 2. The six-vertex model in the anti-ferroelectric regime
• 3. Solvability and Symmetry
• 4. Correlation functions—physical derivation
• 5. Level one modules and bosonization
• 6. Vertex operators
• 7. Space of states—mathematical picture
• 8. Traces of vertex operators
• 9. Correlation functions and form factors
• 10. The $XXX \lim {q \to 1}$
• 11. Discussions
• 13. A. List of formulas
• The book provides a very clear exposition on the subject, and meanwhile gives an elementary introduction to representation theory … serves very well as both introduction and reference.

Mathematical Reviews
• Very clearly written … suitable for those who may not be expert either in quantum groups or in the theory of solvable lattice models.

Zentralblatt MATH
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.