Mean-field theory
Approximation of physical behavior / From Wikipedia, the free encyclopedia
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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 (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.
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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.[1] 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,[2] artificial intelligence, epidemic models,[3] queueing theory,[4] computer-network performance and game theory,[5] as in the quantal response equilibrium[citation needed].