[physicsyogi]

When I was in grad school, we used MH to compute 400-dimensional integrals. We computed ground state and excited state properties of a particular system, using a wavefunction as the probability distribution. This was easily parallelized.

e.g http://phya.snu.ac.kr/~gsjeon/Primary/Abstract/abs26.html

While I can't say that one guess communicated with others, I can say that whenever I moved one particle, the others knew about it immediately because the wavefunction described a strongly correlated system. Communication between guesses sounds really interesting though. I've been out of the game for a while, so I'll have to look that up.

[stellographer]

Check out this guy's work for some really cool examples: http://en.wikipedia.org/wiki/Xin-She_Yang