and 
Consider a spin-spin correlation function at zero field of the form
If 
and 
occupy lattice sites at positions
and 
, respectively, then at large spatial
separation, with 
, the correlation
function depends only r and decays exponentially according to
for 
. The quantity 
is called the correlation length.
Since, as a critical point is approached from above, long range
order sets in, we expect to diverge as 
.
The divergence is characterized by an exponent such that
At 
, the exponential dependence of G(r) becomes 1,
and G(r) decays in a manner expected for a system with long range
order, i.e., as some small inverse power of r. The exponent
appearing in the expression for G(r) characterizes
this decay at .
The exponents, and cannot be determined from MFT, as
MFT neglects all correlations. In order to calculate these
exponents, a theory is needed that restores fluctuations at
some level. One such theory is the so called Landau-Ginzberg
theory. Although we will not discuss this theory in great detail,
it is worth giving a brief introduction to it.