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coding away the hours...

Ok, I take back anything I said about my job this summer not being as interesting as it could be. I'm already lovin' it! I lost myself in my coding today and when I came to after several hours, I'd created some stunning visuals...

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 &Phi4 theory. Apparently, what I'm working on has a lot more relevance to high energy particle theory than I realized. &Phi4 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.


( 3 comments — Leave a comment )
Jun. 16th, 2004 11:33 pm (UTC)
I'm definitely going to pick your brain when I get down there - looks like fun stuff! :) I'll trade ya - I can tell you all about φ4-theory, and you can tell me all about your Ising project, and all this finite size stuff.
Jun. 17th, 2004 11:13 am (UTC)
I'd love to know more about &Phi4 theory. It's definitely the weakest point in my understanding of this. Here's the gist of what I've been reading about...


"Thus a numerical study of finite size scaling in the Ising model serves as a non-perturbative test of triviality of &Phi44-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 too trivial, otherwise it would be easy to test for :)
Jun. 17th, 2004 11:26 am (UTC)
"Trivial" often means "free" in the context of QFT - a free QFT is a pretty damn boring one (there are no interactions, everything is just plane waves... boring!).

For &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).
( 3 comments — Leave a comment )


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