Kinetic growth walk on critical percolation clusters and lattice animals

The statistics of recently proposed kinetic growth walk (KGW) model for linear polymers (or growing self avoiding walk (GSAW)) on two dimensional critical percolation clusters and lattice animals are studied using real-space renormalization group method. The correlation length exponents 's are found to be _KGW ^Pc = 0.68 and _KGW ^LA respectively for the critical percolation clusters and lattice animals. Close agreements are found between these results and a generalized Flory formula for linear polymers at theta point _KGW ^F = 2/ +1),, where is the fractal dimension of the fractal objectF.