Erratum to ‘Statistical topology of perturbed two-dimensional lattices (2016 <i>J. Stat. Mech</i>. P043103)

Leipold, Hannes; Lazar, Emanuel A.; Brakke, Kenneth A.; Srolovitz, David J.

doi:10.1088/1742-5468/aa78af

Cited by 1 publication

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“…The Voronoi constructions allows to estimate the (averaged) distribution of the number of neighbors for particles in each layer [70]; we denote the probability (as calculated from the MC simulations) that a particle has n neighbours in layer α by p α (n).…”

Section: E Bond Orientational Order Parametersmentioning

confidence: 99%

“…In Ref. [70], the distribution of the number of neighbors for a square lattice under an infinitesimal perturbation of the lattice position was computed; the numerical evaluation of these analytical results yield: p(4) = p(8) 0.044, p(5) = p(7) 0.2435 and p(6) 0.4249. The corresponding values extracted from our MC simulations are in good agreement with these predictions: p(4) = p(8) 0.01, p(5) = p(7) 0.22.…”

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The asymmetric Wigner bilayer

Antlanger

Kahl

Mazars

et al. 2018

The Journal of Chemical Physics

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We present a comprehensive discussion of the so-called asymmetric Wigner bilayer system, where mobile point charges, all of the same sign, are immersed into the space left between two parallel, homogeneously charged plates (with possibly different charge densities). At vanishing temperatures, the particles are expelled from the slab interior; they necessarily stick to one of the two plates, and form there ordered sublattices. Using complementary tools (analytic and numerical) we study systematically the self-assembly of the point charges into ordered ground state configurations as the inter-layer separation and the asymmetry in the charge densities are varied. The overwhelming plethora of emerging Wigner bilayer ground states can be understood in terms of the competition of two strategies of the system: the desire to guarantee net charge neutrality on each of the plates and the effort of the particles to self-organize into commensurate sublattices. The emerging structures range from simple, highly commensurate (and thus very stable) lattices (such as staggered structures, built up by simple motives) to structures with a complicated internal structure. The combined application of our two approaches (whose results agree within remarkable accuracy) allows to study on a quantitative level phenomena such as over-and underpopulation of the plates by the mobile particles, the nature of phase transitions between the emerging phases (which pertain to two different universality classes), and the physical laws that govern the long-range behaviour of the forces acting between the plates. Extensive, complementary Monte Carlo simulations in the canonical ensemble, which have been carried out at small, but finite temperatures along selected, well-defined pathways in parameter space confirm the analytical and numerical predictions within high accuracy. The simple setup of the Wigner bilayer system offers an attractive possibility to study and to control complex scenarios and strategies of colloidal self-assembly, via the variation of two simple system parameters.arXiv:1808.07345v1 [cond-mat.soft] 22 Aug 2018 2

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Section: E Bond Orientational Order Parametersmentioning

confidence: 99%

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confidence: 99%