# A Why does Finite Size Scaling shift the Phase Transition Down?

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1. Aug 2, 2016

### georgeD123

See the title. I'm not sure that this is the right place to post this question, but I'm not sure it fits any better on any of the other boards.

Let's say you have a phase transition. The correlation length will scale as:

ξ = |TC-T|ν

This diverges on both sizes of the phase transition. Now, the finite size scaling theory says to replace ξ with L, since that is the largest the correlation length can be in a real system with finite size, and solve for what temperature that occurs at.

You get two temperatures! One above TC and one below. Obviously, the temperature has to shift down; if it didn't, we would have no phase transitions in bulk materials, since we would be always below the critical temperature. However, this seems like an argument against using finite scaling theory at all, as much as an argument to only consider the lower temperature.

If anybody understands this better than I do, I would love some help understanding!

2. Aug 7, 2016