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Approximation of physical behavior
In physics and probability theory, mean-field theory (MFT) or self-consistent field theory studies the behavior of high-dimensional random (stochastic)
Mean-field_theory
Study of strategic decision making
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
Mean-field_game_theory
Method to determine the electronic structure of strongly correlated materials
Dynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation
Dynamical_mean-field_theory
Quantum field theory enjoying conformal symmetry
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional
Conformal_field_theory
Approximation method in quantum physics
energy of the system. Hartree–Fock approximation is an instance of mean-field theory, where neglecting higher-order fluctuations in order parameter allows
Hartree–Fock_method
Parameter describing physics near critical points
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
Critical_exponent
Physical model defined on a lattice
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
Lattice_model_(physics)
Structure of the atomic nucleus
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
Nuclear_structure
Model of interacting spinless bosons on a lattice
determined by calculating the energy of this mean-field Hamiltonian using second-order perturbation theory and finding the condition for which ψ ≠ 0 {\displaystyle
Bose–Hubbard_model
Describes the range of energies of an electron within the solid
can be treated non-perturbatively within the so-called dynamical mean-field theory, which attempts to bridge the gap between the nearly free electron
Electronic_band_structure
State of matter with properties of both conventional liquids and crystals
neighboring molecules, and the theory then considers a mean-field average of the interaction. Solved self-consistently, this theory predicts thermotropic nematic-isotropic
Liquid_crystal
Physical quantities taking values at each point in space and time
methods. One important example is mean field theory. Classical fields as above, such as the electromagnetic field, are usually infinitely differentiable
Field_(physics)
Criterion in mean field theory
Mean field theory gives sensible results as long as one is able to neglect fluctuations in the system under consideration. If ϕ {\displaystyle \phi }
Ginzburg_criterion
French physicist (1865–1940)
theory of ferromagnetism in 1907. Weiss domains and the Weiss magneton are named after him. Weiss also developed the molecular or mean field theory,
Pierre_Weiss
Mathematical study of waiting lines, or queues
formula for the mean waiting time in a G/G/1 queue, now known as Kingman's formula. Leonard Kleinrock worked on the application of queueing theory to message
Queueing_theory
German physicist
Werner state, finitely correlated states aka matrix product states, mean field theory and entanglement area laws. After studies from 1970 - 1982 at the
Reinhard_F._Werner
Model in theoretical ecology and statistical mechanics
calculation. The cavity method can also be used to derive a dynamical mean-field theory model for the dynamics. The cavity calculation yields a self-consistent
Random generalized Lotka–Volterra model
Random_generalized_Lotka–Volterra_model
Collection of models with the same renormalization group flow limit
critical exponents stabilize and can be calculated by an analog of mean-field theory (this dimension is d ∗ = 4 {\displaystyle d^{*}=4} for Ising or for
Universality_class
Topics referred to by the same term
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
Self-consistent_mean_field
Regularization method for artificial neural networks
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
Dropout_(neural_networks)
Smallest length scales in turbulent fluid flow
}{\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
Kolmogorov_microscales
Problem in physics and quantum mechanics
plasma) Mean-field theory and extensions (e.g. Hartree–Fock, Random phase approximation) Dynamical mean field theory Many-body perturbation theory and Green's
Many-body_problem
uses mean field theory and is based on Peierls' inequality. Bilbro, G.L.; Snyder, W.E.; Garnier, S.J.; Gault, J.W. (Jan 1992). "Mean field annealing:
Mean_field_annealing
American physicist and author
Dynamical Mean-Field Theory Approach, won the 2009 Alpha Sigma Nu best book prize for physical science. He generalized dynamical mean-field theory into nonequilibrium
James_K._Freericks
Theory of continuous phase transitions
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
Landau_theory
Thin layer of liquid in a superfluid state
three or more dimensions one must resort to a mean field theory approach. [dubious – discuss] The theory of superfluid transitions in two dimensions is
Superfluid_film
Equation in mathematical queueing theory
the mean arrival time) and cs is the coefficient of variation for service times. Shanthikumar, J. G.; Ding, S.; Zhang, M. T. (2007). "Queueing Theory for
Kingman's_formula
Matrix-valued random variable
matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory, diagrammatic
Random_matrix
Microscopic theory of superconductivity
many-body theory meeting at the Stevens Institute of Technology, Schrieffer thought of the idea of using a statistical approach analogous to a mean field, because
BCS_theory
State of matter
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
Bose–Einstein_condensate
Fermi systems. Vollhardt is one of the founders of the Dynamical Mean-Field Theory (DMFT) for strongly correlated materials such as transition metals
Dieter_Vollhardt
Stochastic process in probability theory
deviation of the empirical distribution function from its expectation. In mean field theory, limit theorems (as the number of objects becomes large) are considered
Empirical_process
Probabilistic algorithms to simulate quantum many-body systems
complex many-body effects encoded in the wave function, going beyond mean-field theory. In particular, there exist numerically exact and polynomially-scaling
Quantum_Monte_Carlo
French mathematician (1949–2010)
with S. Jon Chapman and Jacob Rubinstein, Schatzmann developed a mean-field theory of the vorticity density of superconductivity vortices, now called
Michelle_Schatzman
Dimensionality of space at which the character of the phase transition changes
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
Critical_dimension
Method of improving artificial neural network
Samuel S. (2019). "A Mean Field Theory of Batch Normalization". arXiv:1902.08129 [cs.NE]. Knyazev, Neymeyr (2003). "A geometric theory for preconditioned
Batch_normalization
Computational quantum mechanical modelling method to investigate electronic structure
the standard diffusion equation. Basis set (chemistry) Dynamical mean field theory Gas in a box Harris functional Kohn–Sham equations Local density approximation
Density_functional_theory
Equation in solid state physics
These approximation is the result of a mean-field theory that describes one electron interacting with a field that is the result of averaging the position
Hartree_equations
French physicist
University and together they developed today's formulation of Dynamical Mean Field Theory by mapping it onto the self-consistent solution of a quantum impurity
Antoine_Georges
Characteristic length in a superconductor
, where α 0 {\displaystyle \alpha _{0}} is a constant. In Landau mean-field theory, at temperatures T {\displaystyle T} near the superconducting critical
Superconducting coherence length
Superconducting_coherence_length
Topics referred to by the same term
non-profit organization Marriage and Family Therapist Mean-field theory, in physics and probability theory Micro Four Thirds system, a lens mount for mirrorless
MFT
Numerical technique for solving quantum Hamiltonians
optimization problem. Can be used as an impurity solver for Dynamical mean-field theory techniques. When combined with finite size scaling, estimating the
Exact_diagonalization
Concept in condensed matter physics
virtual particles. In other words, every type of mean-field kinetic equation, and in fact every mean-field theory, involves a quasiparticle concept. This section
Quasiparticle
Mathematical model of ferromagnetism in statistical mechanics
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
Ising_model
The self-consistent mean field (SCMF) method is an adaptation of mean field theory used in protein structure prediction to determine the optimal amino
Self-consistent mean field (biology)
Self-consistent_mean_field_(biology)
Physical process
gravity and no energy is being dissipated. A high dimensional limit mean-field theory for jamming was obtained by Giorgio Parisi and Francesco Zamponi,
Jamming_(physics)
Disordered magnetic state
Covers mean field theory, experimental data, and numerical simulations. Mezard, Marc; Parisi, Giorgio; Virasoro, Miguel Angel (1987), Spin glass theory and
Spin_glass
Argentine condensed matter physicist
relaxation (with J. Kurchan and L. Peliti); the development of a mean-field theory for the relaxation of open quantum disordered systems (with G. Lozano);
Leticia_Cugliandolo
Lattice model of polymer solutions
approximated by the mean-field theory. One well-studied effect on interaction energies neglected by unmodified Flory–Huggins theory is chain correlation
Flory–Huggins_solution_theory
Theorem in queueing theory
In mathematical queueing theory, Little's law (also result, theorem, lemma, or formula) is a theorem by John Little which states that the long-term average
Little's_law
Simplified model in condensed matter physics
mean-field theory Stoner criterion Altland, A.; Simons, B. (2006). "Interaction effects in the tight-binding system". Condensed Matter Field Theory.
Hubbard_model
Type of exotic matter
{\displaystyle H=H_{0}+H_{\rm {int}}} . In Gross-Pitaevskii mean field theory, one replaces the field operators with c-number functions: ψ ^ m ( r ) → ψ m (
Spinor_condensate
Scheduling algorithm, the first piece of data inserted into a queue is processed first
In computing and in systems theory, first in, first out (the first in is the first out), acronymized as FIFO, is a method for organizing the manipulation
FIFO (computing and electronics)
FIFO_(computing_and_electronics)
Mathematical identity in queueing theory
In queueing theory, a discipline within the mathematical theory of probability, the Pollaczek–Khinchine formula states a relationship between the queue
Pollaczek–Khinchine_formula
Type of magnetic phenomenon
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
Ferrimagnetism
Superconductive behavior at temperatures much higher than absolute zero
explanations assume that superconductive properties can be treated by mean-field theory. It also does not consider that in addition to the superconductive
High-temperature superconductivity
High-temperature_superconductivity
Branch of physics
developed a mean-field theory for continuous phase transitions, which described ordered phases as spontaneous breakdown of symmetry. The theory also introduced
Condensed_matter_physics
Type of queue model in queueing theory
In queueing theory, a discipline within the mathematical theory of probability, an M/M/1 queue represents the queue length in a system having a single
M/M/1_queue
Statistical theory
Information field theory (IFT) is a Bayesian statistical field theory relating to signal reconstruction, cosmography, and other related areas. IFT summarizes
Information_field_theory
State of matter
Chronicle". news.cornell.edu. Yu, Xiaoquan; Mueller, Markus (2012). "Mean field theory of superglasses". Physical Review B. 85 (10) 104205. arXiv:1111.5956
Supersolid
Materials with electrical properties that cannot be explained by non-interacting entities
being in a "sea" of the averaged motion of the others (also known as mean field theory). Each single electron has a complex influence on its neighbors. The
Strongly_correlated_material
Electrical insulators that are conventionally expected to be conductors
insulator as U is increased, can be predicted within the dynamical mean field theory. Mott reviewed the subject in 1968. The subject has been thoroughly
Mott_insulator
of polarisation bubbles connected by interaction lines). Dynamical mean field theory is equivalent to taking only purely local diagrams into account: Φ
Luttinger–Ward_functional
Isotope of helium
helium - Cornell Chronicle". Yu, Xiaoquan; Mueller, Markus (2012). "Mean field theory of superglasses". Physical Review B. 85 (10) 104205. arXiv:1111.5956
Helium-4
Technique for setting initial values of trainable parameters in a neural network
Samuel; Pennington, Jeffrey (2018-07-03). "Dynamical Isometry and a Mean Field Theory of CNNs: How to Train 10,000-Layer Vanilla Convolutional Neural Networks"
Weight_initialization
Probability theory concept
In queueing theory, a discipline within the mathematical theory of probability, the G/G/1 queue represents the queue length in a system with a single
G/G/1_queue
Nuclear physicist (born 1943)
systems, with his publications including journal papers and the book Mean Field Theory, co-authored with Vladimir M. Kolomietz. He has been awarded the S
Shalom_Shlomo
Condensed matter physics model involving only closed loops
1103/physrevlett.66.1773. ISSN 0031-9007. PMID 10043303. Xiao-Gang Wen, Mean Field Theory of Spin Liquid States with Finite Energy Gaps and Topological Orders
String-net_liquid
Physical phenomenon
system without disorder is well captured within Extended Dynamical Mean Field Theory (EDMFT) supported by Metropolis Monte Carlo simulations. Direct experimental
Coulomb_gap
Supposition or system of ideas intended to explain something
theory — Field theory — Galois theory — Game theory — Gauge theory — Graph theory — Group theory — Hodge theory — Homology theory — Homotopy theory — Ideal
Theory
Measure of electrostatic effect and how far it persists
n_{j}(\mathbf {r} )} may be considered, under the assumptions of mean field theory, to tend toward the Boltzmann distribution, n j ( r ) = n j 0 exp
Debye_length
Mathematical limit applied in statistical physics
{\displaystyle n\to 0} typically introduces many subtleties. When using mean-field theory to perform one's calculations, taking this limit often requires introducing
Replica_trick
Multi-server queueing model
In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang–C model) is a multi-server queueing model.
M/M/c_queue
Statistical model in quantum mechanics of magnetic materials
watershed moment—representing the transition from ″approximate theories″ (such as mean-field theory) to ″exact solutions.″ This breakthrough eventually led Nobel
Quantum_Heisenberg_model
Type of plot in condensed matter physics
technique for studying magnetism in 1957. According to the Landau theory applied to the mean field picture for magnetism, the free energy of a ferromagnetic material
Arrott_plot
Physical theory with fields invariant under the action of local "gauge" Lie groups
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local
Gauge_theory
American mathematician (born 1937)
Propagators and the Stability of Mean Field Theory", in Jaffe, Arthur; Lehmann, Harry; Mack, Gerhard (eds.), Quantum Field Theory: A Selection of Papers in Memoriam
Arthur_Jaffe
A polymer field theory is a statistical field theory describing the statistical behavior of a neutral or charged polymer system. It can be derived by transforming
Polymer_field_theory
Study of computable functions and Turing degrees
overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: What does it mean for a function
Computability_theory
Physical process of transition between basic states of matter
Some model systems do not obey a power-law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition
Phase_transition
Algebraic structure with addition, multiplication, and division
operations on rational numbers do. Fields are fundamental algebraic structures that are widely used in algebra, number theory, and many other areas of mathematics
Field_(mathematics)
Aspect of queueing theory
In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are Markovian (modulated
M/G/1_queue
Physics of many interacting particles
include many problems in a wide variety of fields such as biology, neuroscience, computer science, information theory and sociology. Its main purpose is to
Statistical_mechanics
Concept in physics
other theoretical models for SOC have been based upon information theory, mean field theory, the convergence of random variables, and cluster formation. A
Self-organized_criticality
Temperature and pressure point where phase boundaries disappear
p_{\text{c}}={\frac {a}{27b^{2}}}.} However, the van der Waals equation, based on a mean-field theory, does not hold near the critical point. In particular, it predicts
Critical point (thermodynamics)
Critical_point_(thermodynamics)
Theoretical model in physics
Erik; Lichtenstein, Alexander; Vollhardt, Dieter (eds.). Dynamical Mean-Field Theory of Correlated Electrons. Verlag des Forschungszentrum Jülich. ISBN 978-3-95806-619-9
Fermi_liquid_theory
System for describing queueing models
In queueing theory, a discipline within the mathematical theory of probability, Kendall's notation (or sometimes Kendall notation) is the standard system
Kendall's_notation
Perturbative analysis of quantum field theories
matter physics where it can be used to provide a rigorous basis for mean-field theory. This expansion technique was first introduced by Gerard 't Hooft
1/N_expansion
Scale-free network generation algorithm
6988. Fronczak, Agata; Fronczak, Piotr; Hołyst, Janusz A (2003). "Mean-field theory for clustering coefficients in Barabasi-Albert networks". Phys. Rev
Barabási–Albert_model
Stochastic diffusion process in probability theory
conditions, the mean-field process just defined will converge to the corresponding McKean-Vlasov process. Mean-field theory Mean-field game theory Random matrices:
McKean–Vlasov_process
Model in statistical physics
varying mean field. The field is defined as the average spin value over a large region, but not so large so as to include the entire system. The field still
High-dimensional_Ising_model
Two closely related models for generating random graphs
In the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
special circumstances. While traditional mean-field theory predictions suggest the value of 1.5, more advanced mean-field investigations have demonstrated that
Dislocation_avalanches
Deviation of a physical system from being a harmonic oscillator
the atoms within a mean-field theory. Finally, it is possible to use Møller–Plesset perturbation theory to go beyond the mean-field formalism. Consider
Anharmonicity
Queue model
In queueing theory, a discipline within the mathematical theory of probability, an M/G/k queue is a queue model where arrivals are Markovian (modulated
M/G/k_queue
Field theory of scalar fields
physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under
Scalar_field_theory
Discipline within mathematical theory
In queueing theory, a discipline within the mathematical theory of probability, the G/M/1 queue represents the queue length in a system where interarrival
G/M/1_queue
Chemical compound
corrected density functional theory, the DFT+ Hubbard U method, the GW approximation, DFT + dynamical mean-field theory (DMFT), and hybrid exchange-correlation
Nickel(II)_oxide
Aspect of mathematical queueing theory
In queueing theory, a discipline within the mathematical theory of probability, an M/D/1 queue represents the queue length in a system having a single
M/D/1_queue
Physics award
(2016-01-05). "Samuel Frederick Edwards: Founder of modern polymer and soft matter theory". Proceedings of the National Academy of Sciences. 113 (1): 10–11. Bibcode:2016PNAS
Boltzmann_Medal
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