Domain Growth on Percolation Structures

We discuss the dynamics of phase transformations following a quench from a high-temperature disordered state to a state below the critical temperature in the case in which the system is not translationally invariant. In particular, we consider the ordering dynamics for deterministic fractal substrates and for percolation networks by means of two models and for both a non-conserved order parameter and a conserved order parameter. The first model of phase separation employed contains a spherical 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) tlidw in the non-conserved case and as R(t)N t’/2ci%i‘nvthe conserved case. Instead, the height of the peak of the structure factor increases as t“”* and tJ”‘ respectively. These exponents are related to the random walk exponent dwand to the spectral dimension d, 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 percolation threshold. We consider the growth laws for the domain size R ( t ) and the droplet size distribution.