Mean-field theory

Summary

Mean-field theory approximates a system of many interacting parts by independent parts, each of which feels only the average effect of the others. For a lattice spin system it replaces the Gibbs measure by the best product measure, which leads to a self-consistency equation for the magnetization. It is exact for models in which every spin interacts weakly with all others. For short-range models, it gives the correct critical behaviour above the upper critical dimension. It is the first approximation used for a new model and gives a first picture of its phase diagram.