If you’re interested in learning about statistical mechanics, graphical models, information theory, error-correcting codes, belief propagation, constraint satisfaction problems, or the connections between all those subjects, you should know about a couple of books that should be out soon, but for which you can already download extensive draft versions.

The first is Information, Physics, and Computation by Marc Mézard and Andrea Montanari.

The second is Modern Coding Theory by Tom Richardson and Ruediger Urbanke.

I also recommend the tutorial on Modern Coding Theory: the Statistical Mechanics and Computer Science Points of View, by Montanari and Urbanke, from the lectures they gave at the 2006 Les Houches summer school.