Magnetic hierarchical deposition

Anna I. Posazhennikova and Joseph O. Indekeu

Physica A: Statistical Mechanics and its Applications, 2014, vol. 414, issue C, 240-248

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.

Keywords: Deposition model; Fractal; Magnetic interaction; Roughness (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437114005962
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:414:y:2014:i:c:p:240-248

DOI: 10.1016/j.physa.2014.07.027

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().