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.
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.
This is a late response. Here are some more