The extension of Landau theory to include fluctuations in the order parameter shows that Landau theory is only strictly valid near the critical points of ordinary systems with spatial dimensions higher than 4. This is the upper critical dimension, and it can be much higher than four in more finely tuned phase transition. In Mukhamel 's analysis of the isotropic Lifschitz point, the critical dimension is 8. This is because Landau theory is a mean field theory, and does not include long-range correlations.