TIME-DEPENDENT GINZBURG-LANDAU MODEL IN THE ABSENCE OF TRANSLATIONAL INVARIANCE - NONCONSERVED ORDER-PARAMETER DOMAIN GROWTH

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 agree ment 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 w ith 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 R(t) similar to t(z) and relates this exponent to the three expone nts which characterize the static and dynamical properties of fractal structures, namely the fractal dimension of the lattice d(f), the rand om walk dimension d(w) and the spectral dimension d(s). We also presen t a brief renormalization group treatment of the model. Finally, we ha ve considered lattices with infinite ramification numbers which have s pectral dimensions larger that 2 and show a finite temperature phase t ransition.