What is Mean field theory: Definition and 12 Discussions

In physics and probability theory, mean-field theory (aka MFT or rarely self-consistent field theory) studies the behavior of high-dimensional random (stochastic) 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 consider many individual components that interact with each other. In MFT, the effect of all the other individuals on any given individual is approximated by a single averaged effect, thus reducing a many-body problem to a one-body problem.
The main idea of MFT is to replace all interactions to any one body with an average or effective interaction, sometimes called a molecular field. This reduces any many-body problem into an effective one-body problem. The ease of solving MFT problems means that some insight into the behavior of the system can be obtained at a lower computational cost.
MFT has since been applied to a wide range of fields outside of physics, including statistical inference, graphical models, neuroscience, artificial intelligence, epidemic models, queueing theory, computer-network performance and game theory, as in the quantal response equilibrium.

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  1. josephsanders

    High Energy Literature for introduction to O(N) vector model

    TL;DR Summary: Looking for literature on O(N) vector model Hello, We have been going over the O(N) vector model in my QFT class but the notes are not very detailed and we are not using a textbook. Does anyone know of a good QFT book which goes over this material? I have a copy of Shrednicki...
  2. J

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    I have a problem about Heisenberg model.When applying mean field approximation,why does the average of spin flip terms be zero(<S+>=<S-> = 0 )? Thanks
  3. B

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  5. Xenosum

    Mean Field Theory for Fermions/Bosons

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  6. B

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  7. H

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  8. B

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  9. C

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  10. maverick280857

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  11. T

    Why Is Fourier Transform Used in Diagonalizing Operators in Mean Field Theory?

    Hi... I hope somebody can help me... Studying mean field theory in a passage it was necessary to calcolate the inverse of this operator defined on Z^2: $A(I,K)=-J\sum_e \delta(I,K-e)+1/(\beta)*\delta(I,K)$ where I,K pass all ZxZ and the sum on $e$ is a sum on the for basis vectors...
  12. S

    Mean Field Theory: Get Book Recommendations

    I have just started reading up on mean field theory. Any book you could refer??
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