My code simulates a hypercubic lattice of correlated spins in an arbitrary number of dimensions, but this is a snapshot for a 2-d case. It's just after the system has come to equilibrium near its critical temperature. The chaotic regions you see are spin clusters... aka, magnetic domains.

I also read a good bit of two papers today on finite size scaling in &Phi

^{4}theory. Apparently, what I'm working on has a lot more relevance to high energy particle theory than I realized. &Phi

^{4}is a quantum field theory, but if you use it with an O(1) symmetry group, it's isomorhpic to the Ising model (what I used to generate the picture above)... which just blows my mind! I think I got very lucky this summer.

## Comments

pbrane^{4}-theory, and you can tell me all about your Ising project, and all this finite size stuff.spoonless^{4}theory. It's definitely the weakest point in my understanding of this. Here's the gist of what I've been reading about...http://arxiv.org/abs/hep-lat/0405023

"Thus a numerical study of finite size scaling in the Ising model serves as a non-perturbative test of triviality of &Phi

^{4}_{4}-theories for all N.One thing I want to know is, what does "triviality" mean in the context of quantum field theories? It must not be

tootrivial, otherwise it would be easy to test for :)pbraneFor &ph;

^{4}-theory, there is the perturbatively well known result that the theory is the opposite of asymptotically free: at large *separations* the coupling goes to zero (the free value), as opposed to in QCD, where at large *energies* the coupling goes to zero.In QCD, this is checked experimentally by seeing how free the quarks get when slammed together at enormous energies. In non-asymptotically free theories, I guess you have to check for large distance effects - violation of strict scaling laws that would hold if the theory were a conformal field theory (which it sure seems to not be in perturbation theory).