DOMAIN GROWTH ON SELF-SIMILAR STRUCTURES

The behavior of the spherical Ginzburg-Landau model on a class of nont ranslationally invariant, fractal lattices is investigated in the case s of conserved and nonconserved Langevin dynamics. Interestingly, the static and dynamic properties can be expressed by means of three expon ents characterizing these structures: the embedding dimensions d, the random walk exponent d(w), and the spectral dimension d(s). An order-d isorder transition occurs if d(s)>2. Explicit solutions show that the domain size evolves with time as R(t)similar to t(1/dw) in the noncons erved case and as R(t)similar to t(1/2dw) in the conserved case, where as the height of the peak of the structure factor increases in time as t(ds/2) in the first case and as t(ds/4) in the second while the syst em orders. Finally we derive the scaling function for the nonconserved dynamics and the multiscaling function for the conserved dynamics.