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In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic that are free to vary). Such models ...
Dynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials.In such materials, the approximation of independent electrons, which is used in density functional theory and usual band structure calculations, breaks down.
A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according to whether the represented physical quantity is a scalar, a vector, a spinor, or a tensor, respectively. A field has a consistent tensorial character wherever it is defined: i.e. a field cannot be a scalar field somewhere and a vector field ...
Random matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory, diagrammatic methods, the cavity method, or the replica method to compute quantities like traces, spectral densities, or scalar products between eigenvectors.
One of the major discoveries in the study of critical phenomena is that mean field theory of critical points is only correct when the space dimension of the system is higher than a certain dimension called the upper critical dimension which excludes the physical dimensions 1, 2 or 3 in most cases. The problem with mean field theory is that the ...
Hartree–Fock approximation is an instance of mean-field theory, [1] where neglecting higher-order fluctuations in order parameter allows interaction terms to be replaced with quadratic terms, obtaining exactly solvable Hamiltonians. Especially in the older literature, the Hartree–Fock method is also called the self-consistent field method ...
Even when Pierre Weiss did take the mantle of professor at Lyon, he later accepted the ETH Zurich proposal to become physics professor and director of the Institute of Physics in 1902. In 1907, he published an important work on the nature of ferromagnetism where he introduced the concept of molecular field, a precursor idea to mean field theory ...
Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.)