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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.

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Do you have anything specific in mind? I think the term integrability is sometimes used in slightly different contexts. –  Pieter Naaijkens Sep 22 '11 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. –  Eric Zaslow Sep 24 '11 at 17:28

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up vote 18 down vote accepted

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.

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Yes, "exactly solvable" is what I mean. Thanks, I will update my question later. –  Phira Sep 22 '11 at 14:35

Another good recent book:

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