Magnetic hierarchical deposition. / Posazhennikova, Anna; Indekeu, Joseph O.

In: Physica A: Statistical Mechanics and its Applications , Vol. 414, 25.07.2014, p. 240.

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Magnetic hierarchical deposition. / Posazhennikova, Anna; Indekeu, Joseph O.

In: Physica A: Statistical Mechanics and its Applications , Vol. 414, 25.07.2014, p. 240.

Research output: Contribution to journalArticlepeer-review

Harvard

Posazhennikova, A & Indekeu, JO 2014, 'Magnetic hierarchical deposition', Physica A: Statistical Mechanics and its Applications , vol. 414, pp. 240. https://doi.org/10.1016/j.physa.2014.07.027

APA

Posazhennikova, A., & Indekeu, J. O. (2014). Magnetic hierarchical deposition. Physica A: Statistical Mechanics and its Applications , 414, 240. https://doi.org/10.1016/j.physa.2014.07.027

Vancouver

Posazhennikova A, Indekeu JO. Magnetic hierarchical deposition. Physica A: Statistical Mechanics and its Applications . 2014 Jul 25;414:240. https://doi.org/10.1016/j.physa.2014.07.027

Author

Posazhennikova, Anna ; Indekeu, Joseph O. / Magnetic hierarchical deposition. In: Physica A: Statistical Mechanics and its Applications . 2014 ; Vol. 414. pp. 240.

BibTeX

@article{6fd93a0a99734d429b1d251c20e4ceba,
title = "Magnetic hierarchical deposition",
abstract = "We consider random deposition of debris or blocks on a line, with block sizes following a rigorous hierarchy: the linear size equals 1/λn in generation n, in terms of a rescaling factor λ. Without interactions between the blocks, this model is described by a logarithmic fractal, studied previously, which is characterized by a constant increment of the length, area or volume upon proliferation. We study to what extent the logarithmic fractality survives, if each block is equipped with an Ising (pseudo-)spin s = ±1 and the interactions between those spins are switched on (ranging from antiferromagnetic to ferromagnetic). It turns out that the dependence of the surface topology on the interaction sign and strength is not trivial. For instance, deep in the ferromagnetic regime, our numerical experiments and analytical results reveal a sharp crossover from a Euclidean transient, consisting of aggregated domains of aligned spins, to an asymptotic logarithmic fractal growth. In contrast, deep into the antiferromagnetic regime the surface roughness is important and is shown analytically to be controlled by vacancies induced by frustrated spins. Finally, in the weak interaction regime, we demonstrate that the non-interacting model is extremal in the sense that the effect of the introduction of interactions is only quadratic in the magnetic coupling strength. In all regimes, we demonstrate the adequacy of a mean-field approximation whenever vacancies are rare. In sum, the logarithmic fractal character is robust with respect to the introduction of spatial correlations in the hierarchical deposition process.",
author = "Anna Posazhennikova and Indekeu, {Joseph O.}",
year = "2014",
month = jul,
day = "25",
doi = "10.1016/j.physa.2014.07.027",
language = "English",
volume = "414",
pages = "240",
journal = "Physica A: Statistical Mechanics and its Applications ",
issn = "0378-4371",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Magnetic hierarchical deposition

AU - Posazhennikova, Anna

AU - Indekeu, Joseph O.

PY - 2014/7/25

Y1 - 2014/7/25

N2 - We consider random deposition of debris or blocks on a line, with block sizes following a rigorous hierarchy: the linear size equals 1/λn in generation n, in terms of a rescaling factor λ. Without interactions between the blocks, this model is described by a logarithmic fractal, studied previously, which is characterized by a constant increment of the length, area or volume upon proliferation. We study to what extent the logarithmic fractality survives, if each block is equipped with an Ising (pseudo-)spin s = ±1 and the interactions between those spins are switched on (ranging from antiferromagnetic to ferromagnetic). It turns out that the dependence of the surface topology on the interaction sign and strength is not trivial. For instance, deep in the ferromagnetic regime, our numerical experiments and analytical results reveal a sharp crossover from a Euclidean transient, consisting of aggregated domains of aligned spins, to an asymptotic logarithmic fractal growth. In contrast, deep into the antiferromagnetic regime the surface roughness is important and is shown analytically to be controlled by vacancies induced by frustrated spins. Finally, in the weak interaction regime, we demonstrate that the non-interacting model is extremal in the sense that the effect of the introduction of interactions is only quadratic in the magnetic coupling strength. In all regimes, we demonstrate the adequacy of a mean-field approximation whenever vacancies are rare. In sum, the logarithmic fractal character is robust with respect to the introduction of spatial correlations in the hierarchical deposition process.

AB - We consider random deposition of debris or blocks on a line, with block sizes following a rigorous hierarchy: the linear size equals 1/λn in generation n, in terms of a rescaling factor λ. Without interactions between the blocks, this model is described by a logarithmic fractal, studied previously, which is characterized by a constant increment of the length, area or volume upon proliferation. We study to what extent the logarithmic fractality survives, if each block is equipped with an Ising (pseudo-)spin s = ±1 and the interactions between those spins are switched on (ranging from antiferromagnetic to ferromagnetic). It turns out that the dependence of the surface topology on the interaction sign and strength is not trivial. For instance, deep in the ferromagnetic regime, our numerical experiments and analytical results reveal a sharp crossover from a Euclidean transient, consisting of aggregated domains of aligned spins, to an asymptotic logarithmic fractal growth. In contrast, deep into the antiferromagnetic regime the surface roughness is important and is shown analytically to be controlled by vacancies induced by frustrated spins. Finally, in the weak interaction regime, we demonstrate that the non-interacting model is extremal in the sense that the effect of the introduction of interactions is only quadratic in the magnetic coupling strength. In all regimes, we demonstrate the adequacy of a mean-field approximation whenever vacancies are rare. In sum, the logarithmic fractal character is robust with respect to the introduction of spatial correlations in the hierarchical deposition process.

U2 - 10.1016/j.physa.2014.07.027

DO - 10.1016/j.physa.2014.07.027

M3 - Article

VL - 414

SP - 240

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -