Origins of Faceted Anomalous Scaling
Abstract
Fluctuating interfaces are typically characterized by their global, spectral, and local roughness exponents. Faceted anomalous scaling, characterized by αs>1, αs≠α, and αloc=1, owes its name to the tendency of such interfaces to develop long, nearly linear segments called facets. Its statistical origin, and whether facets are required, have remained unclear. We show that this exponent structure is determined by the spatial statistics of the slope field. Slope increments split into typical fluctuations and rare, larger jumps. This anomalous scaling arises either when the typical slope increment displays genuine system-size-dependent anomalous scaling or when the rare jumps dominate the second moment. The two contributions can coexist, and their competition leads to bifractal scaling of the slopes. We establish this framework analytically in the generalized anharmonic Larkin model and the columnar Kardar--Parisi--Zhang equation, and we derive exactly the global, spectral, and local roughness exponents in both cases. The Larkin model realizes both mechanisms and produces anomalous interfaces with or without facets, whereas columnar KPZ belongs to the jump-dominated case and yields αs=3/2.
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BibTeX
@misc{bernard2026origins,
title = {{Origins of Faceted Anomalous Scaling}},
author = {Maximilien Bernard and José Luis Iguain and Alejandro Kolton and Alberto Rosso},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26356},
eprint = {2610.26356},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26356},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Origins of Faceted Anomalous Scaling
AU - Maximilien Bernard
AU - José Luis Iguain
AU - Alejandro Kolton
AU - Alberto Rosso
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.26356
UR - https://arxiv.org/abs/2610.26356
AB - Fluctuating interfaces are typically characterized by their global, spectral, and local roughness exponents. Faceted anomalous scaling, characterized by α_s>1, α_s≠α, and α_loc=1, owes its name to the tendency of such interfaces to develop long, nearly linear segments called facets. Its statistical origin, and whether facets are required, have remained unclear. We show that this exponent structure is determined by the spatial statistics of the slope field. Slope increments split into typical fluctuations and rare, larger jumps. This anomalous scaling arises either when the typical slope increment displays genuine system-size-dependent anomalous scaling or when the rare jumps dominate the second moment. The two contributions can coexist, and their competition leads to bifractal scaling of the slopes. We establish this framework analytically in the generalized anharmonic Larkin model and the columnar Kardar--Parisi--Zhang equation, and we derive exactly the global, spectral, and local roughness exponents in both cases. The Larkin model realizes both mechanisms and produces anomalous interfaces with or without facets, whereas columnar KPZ belongs to the jump-dominated case and yields α_s=3/2.
ER -