2. Basic diffusion propagator in small freq. & wave number limit
Gaussian Propagators
Paramagnon
propagator
spin-singlet
spin-triplet
heat diffusion
Basic diffusion propagator in small freq. & wave number limit

3. Perturbation theory to all orders
3 points vertices
The one-loop renormalization is a finite number (scale like (d-2))
 n-loop skeleton diagrams scale like n(d-2)
4 points vertices
vertex  k2 - GH
renorm. of k dependent part -> finite number
renorm. of  dependent part can give log singularities
HOWEVER one-loop renorm of H from 4-point vertex is identical to that obtained by renormalizing the 2-point vertex

4. Perturbation theory to all orders
2 points vertices
One-loop renormalization of the mixed 2 point vertex
One-loop renormalization of the magnetic 2 point vertex
One-loop renormalization of the fermionic 2 point vertex
Renormalization to all orders
fermionic vertex
magnetization vertex
D(in)=1/GH(i n)
Ds(k, in)=u2 (k, in)/GKt
D(0)=D0[g(ln 1/)]-1
Ds(k 0, 0)=
Ds0(k)d-2[g(2ln kF/k)]-1