Beyond dynamic scaling: rare events break universality
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917380147380224 |
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| author | Marquis, Ulysse Gallotti, Riccardo Barthelemy, Marc |
| author_facet | Marquis, Ulysse Gallotti, Riccardo Barthelemy, Marc |
| contents | Surface growth driven by non-monomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution $P(s)\sim s^{-τ}$. We find that the critical exponents vary continuously with $τ$, recovering Kardar--Parisi--Zhang behavior only for $τ\ge 3$. For $τ<3$, roughness scaling exhibits strong corrections and scale invariance breaks down. We show that this behavior originates from the emergence of a second dynamical length scale $ζ$, corresponding to the linear size of the largest cluster, in addition to the usual correlation length $ξ$. The coexistence of these two relevant scales signals the breakdown of the usual Family--Vicsek scaling. These results point to a new phenomenology of surface growth beyond the standard scale-invariant paradigm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond dynamic scaling: rare events break universality Marquis, Ulysse Gallotti, Riccardo Barthelemy, Marc Statistical Mechanics Disordered Systems and Neural Networks Surface growth driven by non-monomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution $P(s)\sim s^{-τ}$. We find that the critical exponents vary continuously with $τ$, recovering Kardar--Parisi--Zhang behavior only for $τ\ge 3$. For $τ<3$, roughness scaling exhibits strong corrections and scale invariance breaks down. We show that this behavior originates from the emergence of a second dynamical length scale $ζ$, corresponding to the linear size of the largest cluster, in addition to the usual correlation length $ξ$. The coexistence of these two relevant scales signals the breakdown of the usual Family--Vicsek scaling. These results point to a new phenomenology of surface growth beyond the standard scale-invariant paradigm. |
| title | Beyond dynamic scaling: rare events break universality |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2604.01820 |