A numerical study of the statistics of roughness parameters for fluctuating interfaces

Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature disorder their supporting medium, i.e. statistical features its heterogeneities. Different methods have been used to extract roughness information from such self-affine structures, particular exponents associated prefactors. Notably, for an characterization features, it is paramount importance properly assess sample-to-sample fluctuations parameters. Here, by performing analysis based on displacement correlation functions real reciprocal space, we compute As ideal, artifact-free reference case study particularly targeting finite-size consider three cases numerically simulated one-dimensional interfaces: (i) elastic lines under thermal free disorder, (ii) directed polymers equilibrium with disordered energy landscape, (iii) critical depinning state when external applied driving force equals set disorder. Our results shows that rather large measuring exponent. These also relevant amplitudes. Therefore minimum independent interface realizations (at least few tens our numerical simulations) should be guarantee sufficient averaging, issue often overlooked reports.