Had a lunch chat with Clément Hongler, a Columbia friend of Gustavo's who I'd bumped into sporadically in the past. Apparently there are some very weird surprises connecting how Ising-like models behave with, well, take your pick of ADE classification beasties --- dynkin diagrams, cartan matrices, lie algebras, etc. I'm told the current raft of conjectures align the canonical Ising model where you just get spin +1 and -1, pretty much the simplest possible such model I can imagine, with E8, the wackiest (and trendiest!) of the exceptional dynkin diagrams. If I remember correctly E7 then goes with you getting a choice of spin +1 and -1 and 0 being "there is no atom here, don't bother contributing to the energy function for any of my neighbors" and E6 is kinda like (1, ω, ω2, 0) with ω being a cube root of unity. Not that I understand what these correspondences really mean! Something about how fast the correlation function falls off asymptotically. But they sure sound tantalizing.