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.
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
This is a late response. Here are some more