It is often said that above the upper critical dimension, the mean field theory is correct. What is the precise meaning of this statement? Let us be specific and consider the $d$-dimensional Ising model on a hypercubic lattice. It is claimed that the upper critical dimension is $d=4$.
What does this mean?
Does it mean that the mean field theory can get the critical temperature $T_c$ right? Or just the critical exponents right?
