Random deposition with spatially correlated noise (RD-SCN) model: Multi-affine analysis

We study the random deposition model with long-range spatially correlated noise. In this model the particles deposit in a power-law distance of each other as Δi,j=int[u−12ρ], where u is chosen randomly over the range (0,1) and ρ is the correlation strength. The results show that the enhancement of ρ exponent is accompanied by the appearance of irregularities and jumps in the height fluctuations. In spite of scaling exponents dependent to correlation strength in other linear and non-linear growth equations, enhancement of the correlation strength, does not change the growth exponent β=1/2. As the short-range correlations in growth equations result in roughness saturation, the results show that the long-range correlations in this growth model does not saturate the interface width for any system size. The fractal analysis of the height fluctuations performed via the multi-fractal detrended fluctuation analysis (MF-DFA) revealed that the synthetic rough surfaces with ρ=0 are mono-fractal with the Hurst exponent H=0.5. It verifies the un-correlated fluctuations in the simple random deposition model. For the correlation strengths in the range [0,1], the Hurst exponent increases in the range [12,1) with a mono-fractal behavior. In the critical exponent of ρc, multi-affinity is occurred. For ρ>ρc=1 the mono-fractal feature of the height fluctuations tends to the multi-affine one and the strength of multi-affinity increases by enhancement of ρ exponent. The results show that the observed multi-affinity is because of deviation from the normal distribution and appearance of correlations among small and large fluctuations.