One can prove that: k_BT\chi \ll \langle M \rangle^2 Where k_B is the Boltzmann constant, T is the system temperature, \chi is the total magnetic susceptibility and \langle M \rangle is the total average magnetization of the system. Using this in the
Landau theory, which is identical to the mean field theory for the
Ising model, the value of the upper critical dimension comes out to be 4. If the dimension of the space is greater than 4, the mean-field results are good and self-consistent. But for dimensions less than 4, the predictions are less accurate. For instance, in one dimension, the mean field approximation predicts a phase transition at finite temperatures for the Ising model, whereas the exact analytic solution in one dimension has none (except for T=0 and T\rightarrow \infty). ==Example: Classical Heisenberg model==