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## Main Question or Discussion Point

**What's "Wrong" With Landau's Theory of Phase Transitions**

Every book under the sun tells you that the Landau method is wrong because it "fails to consider fluctuations" but I don't see how that's true. It's got a gradient term of the form [tex] (\nabla M )^2 [/tex] and one could then include higher order gradient terms if one wants. How are these gradient terms not a way of allowing fluctuations? I guess my question is if we include terms of all orders in space and temperature (all temperature terms and all gradient terms, to infinite order), where does the Landau approach go "wrong"? Why doesn't it give correct critical exponents?