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Register a new userA numerical study of the statistics of roughness parameters for fluctuating interfaces
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Added by
Sebastian Bustingorry
Publication date
2021
fields
Physics
and research's language is
English
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Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities. Different methods have been used to extract roughness information from such self-affine structures, and in particular their scaling exponents and associated prefactors. Notably, for an experimental characterization of roughness features, it is of paramount importance to properly assess sample-to-sample fluctuations of roughness parameters. Here, by performing scaling analysis based on displacement correlation functions in real and reciprocal space, we compute statistical properties of the roughness parameters. As an ideal, artifact-free reference case study and particularly targeting finite-size systems, we consider three cases of numerically simulated one-dimensional interfaces: (i) elastic lines under thermal fluctuations and free of disorder, (ii) directed polymers in equilibrium with a disordered energy landscape, and (iii) elastic lines in the critical depinning state when the external applied driving force equals the depinning force set by disorder. Our results shows that sample-to-sample fluctuations are rather large when measuring the roughness exponent. These fluctuations are also relevant for roughness amplitudes. Therefore a minimum of independent interface realizations (at least a few tens in our numerical simulations) should be used to guarantee sufficient statistical averaging, an issue often overlooked in experimental reports.
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Ferroic domain walls are known to display the characteristic scaling properties of self-affine rough interfaces. Different methods have been used to extract roughness information in ferroelectric and ferromagnetic materials. Here, we review these different approaches, comparing roughness scaling analysis based on displacement autocorrelation functions in real space, both locally and globally, to reciprocal space methods. This allows us to address important practical issues such as the necessity of a sufficient statistical averaging. As an ideal, artifact-free reference case and particularly targeting finite-size systems, we consider two cases of numerically simulated interfaces, one in equilibrium with a disordered energy landscape and one corresponding to the critical depinning state when the external applied driving force equals the depinning force. We find that the use of the reciprocal space methods based on the structure factor allows the most robust extraction of the roughness exponent when enough statistics is available, while real space analysis based on the roughness function allows the most efficient exploitation of a dataset containing only a limited number of interfaces of variable length. This information is thus important for properly quantifying roughness exponents in ferroic materials.
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