# Mean field models

A **mean field model**, or a **mean field solution** of a model, is an approximation to the actual solution of a model in statistical physics. The model is made exactly solvable by treating the effect of all other particles on a given one as a *mean field* (hence its name). It appear in different forms and different contexts, but all mean field models have this feature in common.

## Mean field solution of the Ising model

A well-known mean field solution of the Ising model goes as follows. From the original hamiltonian,

suppose we may approximate

where is the number of neighbors of site (e.g. 4 in a 2-D squate lattice), and is the (unknown) magnetization: