DOMAIN GROWTH ON PERCOLATION STRUCTURES

We discuss the dynamics of phase transformations following a quench fr om a high-temperature disordered state to a state below the critical t emperature in the case in which the system is not translationally inva riant. In particular, we consider the ordering dynamics for determinis tic fractal substrates and for percolation networks by means of two mo dels and for both a non-conserved order parameter and a conserved orde r parameter. The first model of phase separation employed contains a s pherical constraint which enables us to obtain analytical results for Sierpinski gaskets of arbitrary dimensionality and Sierpinski carpets. The domain size evolves with time as R(t) similar to t(1/dw) in the n on-conserved case and as R(t) similar to t(1/2dw) in the conserved cas e. Instead, the height of the peak of the structure factor increases a s t(ds/2) and t(Ss)/(4) respectively. These exponents are related to t he random walk exponent d(w) and to the spectral dimension d(s) of the Laplace operator on the fractal lattice. The second model studied is generated from a standard Ginzburg-Landau free-energy functional on a Sierpinski carpet and random percolation structures above the percolat ion threshold. We consider the growth laws for the domain size R(t) an d the droplet size distribution.