The Kardar-Parisi-Zhang exponents for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si72.svg"><mml:mrow><mml:mn>2</mml:mn><mml:mo linebreak="badbreak">+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> dimensions

Gomes-Filho, Márcio S.; Penna, A. L. A.; Oliveira, Fernando A.

doi:10.1016/j.rinp.2021.104435

Cited by 21 publications

(24 citation statements)

References 52 publications

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“…In particular we use the SS model, where controlling the probability p we can change the effective noise intensity. The results support recent work [43], which suggest that the effective noise has fractal dimension d f . This fractal dimension is associated with the KPZ exponents from Eq.…”

Section: The Hidden Symmetrysupporting

confidence: 91%

“…For example, the stochastic cellular automaton, etching model [4,7,8], which mimics the erosion process by an acid has been recently proven to belong to the KPZ universality class [67]. Thus, it was used together with the SS model to obtain the fractal dimension and the exponents with a considerable precision [43]. Now, we want to discuss how the fluctuationdissipation theorem is affect by the interface growth.…”

Section: Fluctuations Relations and Fractal Geometrymentioning

confidence: 99%

“…with θ = 0 for d = 1, thus Φ = 1, and a number close to zero for higher dimensions. For 2 + 1 dimensions the etching model yields [43] Φ = 1.00 (2), for other models Φ…”

Section: Fluctuations Relations and Fractal Geometrymentioning

confidence: 99%

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The Fractal Geometry of Growth: Fluctuation–Dissipation Theorem and Hidden Symmetry

et al. 2021

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Growth in crystals can be usually described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics creates a fractal structure at the interface of a crystal and its growth medium, which in turn determines the growth. Recent work by Gomes-Filho et al. (Results in Physics, 104,435 (2021)) associated the fractal dimension of the interface with the growth exponents for KPZ and provides explicit values for them. In this work, we discuss how the fluctuations and the responses to it are associated with this fractal geometry and the new hidden symmetry associated with the universality of the exponents.

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Section: The Hidden Symmetrysupporting

confidence: 91%

Section: Fluctuations Relations and Fractal Geometrymentioning

confidence: 99%

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The Fractal Geometry of Growth: Fluctuation–Dissipation Theorem and Hidden Symmetry

et al. 2021

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“…Recently Anjos et al [28] proposed that the growth dynamics builds up an interface with a fractal dimension d f , which filters the original fluctuations given origin to new fluctuations which, by it turns, yields a new FDT in the fractal space. This allows a possible solution for the KPZ exponents [29]. There is much hope that this approach will drive us to unexpected hidden symmetries and new formulations of the FDT, in line with a visionary comment expressed by Giorio Parisi in the year of physics concept [30].…”

Section: Editorial On the Research Topicmentioning

confidence: 61%

Editorial: The Fluctuation-Dissipation Theorem Today

2022

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“…The violation of the FDT is well-known in the literature, for example, in the KPZ framework [2,33] for d > 1, in structural glass [45] and in ballistic diffusion [46][47][48][49]. Thus, it was proposed [50,51] that, for d + 1 dimensions, the FDT must change to include the fractal dimension of the rough interface connecting the global roughness exponent with the fractal dimension, considering that in a steady-state regime we have a well-defined w s and d f . Thus, for completeness, the correlation between the global exponent α and d f needs to be verified in lattice models.…”

Section: Introductionmentioning

confidence: 99%

Unveiling the connection between the global roughness exponent and interface fractal dimension in EW and KPZ lattice models

Luis¹,

Assis²,

Oliveira³

2022

J. Stat. Mech.

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A connection between the global roughness exponent and the fractal dimension of a rough interface, whose dynamics are expected to be described by stochastic continuum models, still needs more support from simulations in lattice models, which are key to provide completeness for the characterization of a given universality class. In this work, we investigate the asymptotic fractal dimension of interfaces that evolve according to some specific lattice models in d + 1 dimensions (d = 1, 2), which are expected to belong to the Edwards–Wilkinson or Kardar–Parisi–Zhang universality classes. Our results, based on the Higuchi method and on the extrapolation of the effective fractal dimension, allow one to achieve dependence between the asymptotic fractal dimension and global roughness exponent, in which the latter is expected to be hardly accessible for experimentalists. Conversely, we also use a two-points correlation function, which gives the time evolution of the local roughness exponent. As a byproduct, our results suggest that, for d = 1, the fractal dimension converges faster than the global roughness exponents to the asymptotic ones. Therefore, the analysis of the fractal dimension, for d = 1, is suggested to be more accessible than the global roughness exponents to determine the universality class. Corrections for the fractal dimensions in d = 2 were found to be stronger than for d = 1.

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The Kardar-Parisi-Zhang exponents for the 2+1 dimensions

Cited by 21 publications

References 52 publications

The Fractal Geometry of Growth: Fluctuation–Dissipation Theorem and Hidden Symmetry

The Fractal Geometry of Growth: Fluctuation–Dissipation Theorem and Hidden Symmetry

Editorial: The Fluctuation-Dissipation Theorem Today

Unveiling the connection between the global roughness exponent and interface fractal dimension in EW and KPZ lattice models

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