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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.07133 |
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| _version_ | 1866917664175161344 |
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| author | Luis, Edwin E. Mozo Ferreira, Silvio C. de Assis, Thiago A. |
| author_facet | Luis, Edwin E. Mozo Ferreira, Silvio C. de Assis, Thiago A. |
| contents | We introduce a multifractal optimal detrended fluctuation analysis to study the scaling properties of the one-dimensional Wolf-Villain (WV) model for surface growth. This model produces mounded surface morphologies for long time scales (up to $10^9$ monolayers) and its universality class remains controversial. Our results for the multifractal exponent $τ(q)$ reveal an effective local roughness exponent consistent with a transient given by the molecular beam epitaxy (MBE) growth regime and Edward-Wilkinson (EW) universality class for negative and positive $q$-values, respectively. Therefore, although the results corroborate that long-wavelength fluctuations belong to the EW class in the hydrodynamic limit, as conjectured in the recent literature, a bifractal signature of the WV model with an MBE regime at short wavelengths was observed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07133 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bifractality in one-dimensional Wolf-Villain model Luis, Edwin E. Mozo Ferreira, Silvio C. de Assis, Thiago A. Statistical Mechanics We introduce a multifractal optimal detrended fluctuation analysis to study the scaling properties of the one-dimensional Wolf-Villain (WV) model for surface growth. This model produces mounded surface morphologies for long time scales (up to $10^9$ monolayers) and its universality class remains controversial. Our results for the multifractal exponent $τ(q)$ reveal an effective local roughness exponent consistent with a transient given by the molecular beam epitaxy (MBE) growth regime and Edward-Wilkinson (EW) universality class for negative and positive $q$-values, respectively. Therefore, although the results corroborate that long-wavelength fluctuations belong to the EW class in the hydrodynamic limit, as conjectured in the recent literature, a bifractal signature of the WV model with an MBE regime at short wavelengths was observed. |
| title | Bifractality in one-dimensional Wolf-Villain model |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2405.07133 |