If you have a spin system where integrating out spins leads to new interactions ie proliferation, what happens if you go in the other direction and add in more spins? Do you still get proliferation?
Incidentally, it may be said that the difference between high energy physics and condensed matter is in which way round you run renormalisation. In HEP you're trying to figure out the simpler/more symmetric fundamental theory given the low energy behaviour, and in condensed matter you're trying to figure out what the effective (i.e. simple) theory is at low energy, given the high energy "exact" theory (as far as physics at human scale is concerned, we already have the theory of everything in the non-relativistic Schrodinger equation for electrons and nuclei + Couloumb interaction + occasional spin-orbit coupling).
One more thing I don't understand is why in lattice we can only calculate dimensionless quantities, and why it does not make sense to send a dimensionful quantity to 0.
Also, thanks for the informative replies everyone
I thought about your last post a bit more. Please tell me if this is correct:
Does this sound right?
But now let's think about QCD - it too has some cutoff where it stops working. But say we are interested in what its predictions are at a certain scale, let's call it (suggestively :P) a. Then we could make a computer simulation with all the couplings of the theory adjusted to their value at the scale a. And we get some predictions out. And we could compare those predictions with results from a particle accelerator doing experiments at the scale a.
a is exactly analgous here to s in the flashlight-rock example. It is just the length that we experimentally probe the theory to, and the length we put into computers to get the predictions of the theory at that length.
Further, it seems its pretty clear that we can change a - people do calculations on different sized lattices all the time! And further, a is not the scale at which QCD stops working!