In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic)...

intersection of game theory with stochastic analysis and control theory. The use of the term "mean field" is inspired by mean-field theory in physics, which...

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

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional...

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

experimental data. Analytical results can be theoretically achieved in mean field theory in high dimensions or when exact solutions are known such as the two-dimensional...

order to obtain analytic results we often must resort to mean field theory. This mean field may be spatially varying, or global. The configuration space...

neighboring molecules, and the theory then considers a mean-field average of the interaction. Solved self-consistently, this theory predicts thermotropic nematic-isotropic...

can be treated non-perturbatively within the so-called dynamical mean-field theory, which attempts to bridge the gap between the nearly free electron...

nucleon shells according to an approach closer to what is now called mean field theory. Nowadays, it refers to a formalism analogous to the configuration...

determined by calculating the energy of this mean-field Hamiltonian using second-order perturbation theory and finding the condition for which ψ ≠ 0 {\displaystyle...

methods. One important example is mean field theory. Classical fields as above, such as the electromagnetic field, are usually infinitely differentiable...

Mean field theory gives sensible results as long as one is able to neglect fluctuations in the system under consideration. If ϕ {\displaystyle \phi }...

Self-consistent mean field may be one of the following: Mean field theory, an approach to the many-body problem in physics and statistical mechanics Self-consistent...

encountered in the academic research field. In fact, one of the flagship journals of the field is Queueing Systems. Queueing theory is one of the major areas of...

plasma) Mean-field theory and extensions (e.g. Hartree–Fock, Random phase approximation) Dynamical mean field theory Many-body perturbation theory and Green's...

theory of ferromagnetism in 1907. Weiss domains and the Weiss magneton are named after him. Weiss also developed the molecular or mean field theory,...

}{\nu }}=1.} Kolmogorov's 1941 theory is a mean field theory since it assumes that the relevant dynamical parameter is the mean energy dissipation rate. In...

critical exponents stabilize and can be calculated by an analog of mean-field theory (this dimension is 4 for Ising or for directed percolation, and 6...

Interactions shift the value, and the corrections can be calculated by mean-field theory. This formula is derived from finding the gas degeneracy in the Bose...

2011-06-29 at the Wayback Machine of BCS theory as explained by Bob Schrieffer (audio recording) Mean-Field Theory: Hartree-Fock and BCS in E. Pavarini,...

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...

to a tiny uncertainty. This edge-case can be solved exactly with mean field theory. In weak dilution the impact on the weights can be described as w...

describe ferrimagnets, the simplest of which is with mean-field theory. In mean-field theory the field acting on the atoms can be written as H → = H → 0...

complex many-body effects encoded in the wave function, going beyond mean-field theory. In particular, there exist numerically exact and polynomially-scaling...

matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory, diagrammatic...

Samuel S. (2019). "A Mean Field Theory of Batch Normalization". arXiv:1902.08129 [cs.NE]. Knyazev, Neymeyr (2003). "A geometric theory for preconditioned...

Ising model, mean-field Landau theory gives β = 1 / 2 = ν {\displaystyle \beta =1/2=\nu } and so, it (the Ising mean-field Landau theory) is valid only...

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

Covers mean field theory, experimental data, and numerical simulations. Mezard, Marc; Parisi, Giorgio; Virasoro, Miguel Angel (1987), Spin glass theory and...