text: Including long-range correlations Consider the Ising model free energy above. Assume that the order parameter  and external magnetic field, , may have spatial variations. Now, the free energy of the system can be assumed to take the following modified form:
  where  is the total spatial dimensionality. So,
  Assume that, for a localized external magnetic perturbation , the order parameter takes the form . Then,
  That is, the fluctuation  in the order parameter corresponds to the order-order correlation. Hence, neglecting this fluctuation (like in the earlier mean-field approach) corresponds to neglecting the order-order correlation, which diverges near the critical point.
  One can also solve  for , from which the scaling exponent, , for correlation length  can deduced. From these, the Ginzburg criterion for the upper critical dimension for the validity of the Ising mean-field Landau theory (the one without long-range correlation) can be calculated as:
  In our current Ising model, mean-field Landau theory gives  and so, it (the Ising mean-field Landau theory) is valid only for spatial dimensionality greater than or equal to 4 (at the marginal values of , there are small corrections to the exponents). This modified version of mean-field Landau theory is sometimes also referred to as the Landau–Ginzburg theory of Ising phase transitions. As a clarification, there is also a Landau-Ginzburg theory specific to superconductivity phase transition, which also includes fluctuations.