Editing Mean-field theory (section)

==Validity==
In general, dimensionality plays an active role in determining whether a mean-field approach will work for any particular problem. There is sometimes a [[critical dimension]] above which MFT is valid and below which it is not. 

Heuristically, many interactions are replaced in MFT by one effective interaction. So if the field or particle exhibits many random interactions in the original system, they tend to cancel each other out, so the mean effective interaction and MFT will be more accurate. This is true in cases of high dimensionality, when the Hamiltonian includes long-range forces, or when the particles are extended (e.g. [[polymer]]s). The [[Ginzburg criterion]] is the formal expression of how [[thermal fluctuations|fluctuations]] render MFT a poor approximation, often depending upon the number of spatial dimensions in the system of interest.