Abstract
We have determined the static and dynamical properties of the Ginzburg - Landau model, with global coupling of the spherical type, on some non-translationally invariant lattices. Our solutions show that, in agreement with general theorems, fractal lattices with finite ramification do not display a finite temperature phase transition for any embedding dimension, d. On the other hand, the dynamical behaviour associated with the phase ordering dynamics of a non-conserved order parameter is non-trivial. Our analysis reveals that the domain size R grows in time as 
and relates this exponent to the three exponents which characterize the static and dynamical properties of fractal structures, namely the fractal dimension of the lattice 
, the random walk dimension 
and the spectral dimension 
. We also present a brief renormalization group treatment of the model. Finally, we have considered lattices with infinite ramification numbers which have spectral dimensions larger that 2 and show a finite temperature phase transition.