Mean Field Theory
The classical Landau theory (aka mean field theory) values for a scalar field are
If we add derivative terms turning it into a mean field Ginzburg–Landau theory, we get
One of the major discoveries in the study of critical points is that mean field theory is completely wrong in the vicinity of critical points in two and three dimensions. In four dimensions, we have logarithmic corrections.
Read more about this topic: Critical Exponent
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