[honie]

> It's the best introduction to these methods for the mathematically-minded that I've seen, in the sense that it gives quasi-rigorous justifications for a lot of claims, but at the same time doesn't get bogged down in rigor.

Agree! I remember that reference by heart exactly for that reason! :)

> They mention in the book that simultaneous updates with a checkboard are in fact OK.

Yes, the algorithms discussed in the reference were designed to do exactly that. However, and using the Wolff algorithm as an example, in a perfectly checkerboard at low temperature, a cluster would still not grow beyond beyond its confinement. So the initial iterations actually gets reduced to the single-flip Metropolis algorithm under these conditions, but would eventually break most of them and start updating large clusters every iteration. The only time where one would see only two states alternating is at when the simulation temperature approaches 0, where the cluster always covers the entire lattice.