Difference between revisions of "Mean field models"
(I can't believe there was not an entry about this... work in progress)
Revision as of 12:34, 29 April 2010
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: