The more math I read, the more I see concepts from statistical mechanics popping up — all over the place in combinatorics and dynamical systems, but also in geometric situations. So naturally I've been trying to get a grasp on statistical mechanics for a while, but I haven't been very successful. I've skimmed through a couple of textbooks, but they tended to be heavy on the physical consequences and light on the mathematical underpinnings (and even to an extent light on the physical/mathematical intuition, which is inexcusable!)
I suspect that part of the problem is that, unlike the analogous situation with quantum mechanics, I'm not sure what mathematics I can fall back on if I don't "get" some statistical model. So, is there a good resource for statistical mechanics for the mathematically-minded?
Best Answer
A classic book on solvable two-dimensional models is Baxter's "Exactly Solved Models in Statistical Mechanics" now available in a new edition from Dover. The Yang-Baxter equation, of course, has many connections with important branches of mathematics. This book explains its origins and use in solving certain physically motivated models.