# What is a good introduction to integrable models in physics?

I would be interested in a good mathematician-friendly introduction to integrable models in physics, either a book or expository article.

Related MathOverflow question: what-is-an-integrable-system.

• Do you have anything specific in mind? I think the term integrability is sometimes used in slightly different contexts. Sep 22, 2011 at 12:25
• The fact that "integrability" can mean so many things sometimes makes the quest to learn about it so challenging! I have found the introductory sections of Etingoff's paper www-math.mit.edu/~etingof/zlecnew.pdf to be a very good mathematical reference for a particular, physically interesting system (Calogero-Moser) which describes particles interacting in one-dimension. Sep 24, 2011 at 17:28

I take "integrable models" to mean "exactly solvable models in statistical physics".

You can take a look at the classic book

Otherwise this new book is quit readable and covers more than just solvable models

Others can probably give you more mathematician-friendly references, but I think it would be good if you could be more specific about what you are looking for.

• Baxter is a dead link. Aug 28, 2014 at 20:11

My references are very good reviews:

Quantum inverse scattering and Algebraic Bethe Ansatz:

Faddeev: How Algebraic Bethe Ansatz works for integrable model

Kulish and Sklyanin: Quantum Spectral Transform Method. Recent Developments

Takhtajan: Introduction to algebraic Bethe ansatz

and the Books:

Jimbo and Miwa: Algebraic Analysis of Solvable Lattice Models

Korepin et al: Quantum inverse Scattering and Correlation Functions

Korepin et al: The One-Dimensional Hubbard Model

plus the article

Martins and Ramos: The Quantum Inverse Scattering Method for Hubbard-like Models

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• Another good recent book: Maciej Dunajski, Solitons, Instantons and Twistors.

• Some very good reviews on Quantum inverse scattering and Algebraic Bethe Ansatz:

• Faddeev: How Algebraic Bethe Ansatz works for integrable model

• Kulish and Sklyanin: Quantum Spectral Transform Method. Recent Developments

• Takhtajan: Introduction to algebraic Bethe Ansatz

and the Books:

• Jimbo and Miwa: Algebraic Analysis of Solvable Lattice Models

• Korepin et al: Quantum inverse Scattering and Correlation Functions

• Korepin et al: The One-Dimensional Hubbard Model

plus the article

• Martins and Ramos: The Quantum Inverse Scattering Method for Hubbard-like Models

Here are some more