Stacked triangular lattice: Percolation properties

Schrenk, K. J.; Araújo, Nuno A. M.; Herrmann, Hans J.

doi:10.1103/physreve.87.032123

Cited by 17 publications

(13 citation statements)

References 76 publications

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“…In the material PbFe12-xGaxO19, this corresponds to a gallium concentration x = 8.846 (6). We note that the percolation threshold for our realistic model of the magnetic interactions in the hexaferrites is also very close to the threshold for a simple three-dimensional hexagonal stacked structure [14,15]. Fig.…”

supporting

confidence: 66%

Quantum percolation phase transition and magnetoelectric dipole glass in hexagonal ferrites

et al. 2017

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Hexagonal ferrites do not only have enormous commercial impact (£2 billion/year in sales)due to applications that include ultra-high density memories, credit card stripes, magnetic bar codes, small motors and low-loss microwave devices, they also have fascinating magnetic and ferroelectric quantum properties at low temperatures. Here we report the results of tuning the magnetic ordering temperature in PbFe12-xGaxO19 to zero by chemical substitution x. The phase transition boundary is found to vary as ~ − ⁄ / with xc very close to the calculated spin percolation threshold which we determine by Monte Carlo simulations, indicating that the zero-temperature phase transition is geometrically driven. We find that this produces a form of compositionally-tuned, insulating, ferrimagnetic quantum criticality.Close to the zero temperature phase transition we observe the emergence of an electric-dipole glass induced by magneto-electric coupling. The strong frequency behaviour of the glass freezing temperature Tm has a Vogel-Fulcher dependence with Tm finite, or suppressed below zero in the zero frequency limit, depending on composition x. These quantum-mechanical

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confidence: 66%

Quantum percolation phase transition and magnetoelectric dipole glass in hexagonal ferrites

et al. 2017

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“…In general, the existence of three different scaling behaviors in a system often leads to three distinct regimes, as it has been reported in both related [13,14] and unrelated systems (for example see [27,28]). Although there are some similar reports in which the crossover behavior has been investigated by just one crossover exponent [12,[29][30][31], the existence of three regimes clearly can be observed in related figures. Moreover, the proposed scaling ansatz for the systems is not valid in all crossover region.…”

Section: Exponentmentioning

confidence: 71%

Loop-erased random walk on a percolation cluster: Crossover from Euclidean to fractal geometry

Daryaei

Rouhani

2014

Phys. Rev. E

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We study loop-erased random walk (LERW) on the percolation cluster, with occupation probability p ≥ p_{c}, in two and three dimensions. We find that the fractal dimensions of LERW_{p} are close to normal LERW in a Euclidean lattice, for all p>p_{c}. However, our results reveal that LERW on critical incipient percolation clusters is fractal with d_{f}=1.217 ± 0.002 for d=2 and 1.43 ± 0.02 for d=3, independent of the coordination number of the lattice. These values are consistent with the known values for optimal path exponents in strongly disordered media. We investigate how the behavior of the LERW_{p} crosses over from Euclidean to fractal geometry by gradually decreasing the value of the parameter p from 1 to p_{c}. For finite systems, two crossover exponents and a scaling relation can be derived. This work opens up a theoretical window regarding the diffusion process on fractal and random landscapes.

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“…It is well established that the critical point 11 , 13 , 18 , 35 is the infinite system size limit of the percolation threshold p c ( H , L ), which is H -dependent for finite system sizes, L . Furthermore, the expected scaling behavior 10 , 38 , 39 is with ν H = −1/ H 10 , 45 , 46 . Our numerical results in Fig.…”

Section: Resultsmentioning

confidence: 87%

The influence of statistical properties of Fourier coefficients on random Gaussian surfaces

Castro

Luković

Andrade

et al. 2017

Sci Rep

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Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently establish the presence of scale invariance. We show that this symmetry is not affected by the distribution of the modulus of the Fourier coefficients. Furthermore, we investigate the role of the Fourier phases of random surfaces. In particular, we show how the surface is affected by a non-uniform distribution of phases.

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Stacked triangular lattice: Percolation properties

Cited by 17 publications

References 76 publications

Quantum percolation phase transition and magnetoelectric dipole glass in hexagonal ferrites

Quantum percolation phase transition and magnetoelectric dipole glass in hexagonal ferrites

Loop-erased random walk on a percolation cluster: Crossover from Euclidean to fractal geometry

The influence of statistical properties of Fourier coefficients on random Gaussian surfaces

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