In three or more dimensions one must resort to a mean field theory approach.

The goal of mean field theory is to resolve these combinatorial problems.

Physicists often refer to study of the complete graph as a mean field theory.

The formal basis for mean field theory is the Bogoliubov inequality.

In dimensions greater than four, the phase transition of the Ising model is described by mean field theory.

One important example is mean field theory.

This is because Landau theory is a mean field theory.

Mean field theory can be applied to a number of physical systems so as to study phenomena such as phase transitions.

The experimental results can be theoretically achieved in mean field theory for higher-dimensional systems (4 or more dimensions).

This essential simplification of the problem is the cornerstone of mean field theories.

Mean field theory gives sensible results as long as we are able to neglect fluctuations in the system under consideration.

However, the calculation of exact exponents in statistical mechanics showed that mean field theory was not reliable.

As mentioned before, one of the mean field theory hypotheses is that only the two-body interaction is to be taken into account.

The Ginzburg Criterion tells us quantitatively when mean field theory is valid.

Above the upper critical dimension the critical exponents of the theory become the same as that in mean field theory.

An elegant criterion to obtain the critical dimension within mean field theory is due to V. Ginzburg.

The derivations typically rely on a mean field theory approximation to microscopic dynamical equations.

This characteristic feature of the latter theory puts it in the same category as other mean field theories of critical phenomena.

It is also extensively used in condensed matter physics where it can be used to provide a rigorous basis for mean field theory.

Weiss also developed the Molecular or Mean field theory, which is often called Weiss-mean-field theory.

Landau also developed a mean field theory for continuous phase transitions, which described ordered phases as spontaneous breakdown of symmetry.

Among them, Dynamical Mean Field Theory successfully captures the main features of correlated materials.

It was previously used to describe the existence of nucleon shells in the nucleus according to an approach closer to what is now called mean field theory.

In mean field theory, limit theorems (as the number of objects becomes large) are considered and generalise the central limit theorem for empirical measures.

A powerful approximation method is mean field theory, which is a variational method based on the Bogoliubov inequality.