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diagrams that correct the mean-field approximation. In general, dimensionality plays an active role in determining whether a mean-field approach will work for...

{Z_{1}} ),} the above iterative scheme will become the so-called mean field approximation Q ∗ ( Z ) = q ∗ ( Z 1 ) q ∗ ( Z 2 ) , {\displaystyle Q^{*}(\mathbf...

provided by Eq. (7). A standard approximation strategy for polymer field theories is the mean field (MF) approximation, which consists in replacing the...

molecules. The above is simplified further via the application of the mean field approximation, which essentially ignores fluctuations and treats all quantities...

dynamics emerge as a mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics approximation of Bose–Einstein...

wave function and energy of the system. Hartree–Fock approximation is an instance of mean-field theory, where neglecting higher-order fluctuations in...

Dynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of...

The resulting field theories are well-suited for the application of effective approximation techniques, like the mean field approximation. A major difficulty...

electrostatic part of the DLVO interaction is computed in the mean field approximation in the limit of low surface potentials - that is when the potential...

discussing the mean field approximation below. Based on Schwinger's source theory, Steven Weinberg established the foundations of the effective field theory,...

such a model computationally tractable, CRF-infinity employs a mean-field approximation of the postulated novel potential functions (which are driven by...

interaction with all the other particles is taken into account only in a mean field approximation described by ε e f f {\displaystyle \varepsilon _{\mathrm {eff}...

the Hubbard model by applying the mean-field approximation. The particle density operators are written as their mean value ⟨ n i ⟩ {\displaystyle \langle...

predictions are less accurate. For instance, in one dimension, the mean field approximation predicts a phase transition at finite temperatures for the Ising...

exclusively. The critical behavior is usually different from the mean-field approximation which is valid away from the phase transition, since the latter...

hybrid systems. The Poisson–Nernst–Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration...

immediate vicinity of the Curie point, since it is based on a mean-field approximation. Instead, there is a critical behavior of the form χ ∝ 1 ( T −...

Curie's law. The Curie–Weiss law is a simple model derived from a mean-field approximation, this means it works well for the materials temperature, T, much...

the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the...

thermodynamic models of magnetic systems include the Ising model, the mean field approximation, and the ferromagnet to paramagnet phase transition expressed using...