Multifractality of growing surfaces

We have carried out large-scale computer simulations of experimentally motivated (1+1)-dimensional models of kinetic surface roughening with power-law-distributed amplitudes of uncorrelated noise. The appropriately normalized qth-order correlation function of the height differences ${\mathit{c}}_{\mathit{q}}$(x)=〈‖h(x+x’)-h(x’)${\mathrm{\Vert }}^{\mathit{q}}$〉 shows strong multifractal scaling behavior up to a crossover length depending on the system size, i.e., ${\mathit{c}}_{\mathit{q}}$(x)∼${\mathit{x}}_{\mathit{q}}^{\mathit{q}\mathit{H}}$, where ${\mathit{H}}_{\mathit{q}}$ is a continuously changing nontrivial function. Beyond the crossover length, conventional scaling is found.