m(x) is not random variable in the inhomogeneous mean field field theories, 
replacing m(x) with m should be good approximation close to the critical point.  

when take saddle point equation we are getting mean field result because it's replacing phi(x) with phi_0(x),
i.e., just a single path, k.  And all mean field theories (inhomogeneous or homogeneous) are in terms of phi_0(x) = <phi(x)> = m(x).  

The perturbative approach, and self-consistent HF approach allow fluctuations since they incorporate many paths into Z.  
But simple perturbative expansion may not be good at all for large uphi^4, unlike MFT, which can do large phi.  SCHF allows 
large phi, and handles fluctuations better than saddle point/mean field.  But still we need more classes of diagrams in self-energy
than just HF, evidently.  But it does also suggest that the mean field results will work well for d >= 4, and that phase transition
won't happen for d < 2, which is correct.  








