Lattice gas with nearest- and next-to-nearest-neighbor exclusion

Feng, Xin; Blöte, Henk W. J.; Nienhuis, Bernard

doi:10.1103/physreve.83.061153

Cited by 29 publications

(42 citation statements)

References 35 publications

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“…This transition belongs to the Ashkin Teller universality class (see Refs. [25][26][27][28] for recent numerical studies). For k = 2, 3, we find that the system undergoes one continuous transition directly from the I phase to a crystalline S phase.…”

Section: A Phase Diagrammentioning

confidence: 99%

“…When k = 1 (hard squares), the system undergoes a transition into a high * joyjit@imsc.res.in † rrajesh@imsc.res.in density columnar phase. The transition is continuous for m = 2 [24][25][26][27][28], and first order for m = 3 [25]. When m → ∞, keeping k fixed, the lattice model is equivalent to the model of oriented rectangles in two dimensional continuum, also known as the Zwanzig model [29].…”

Section: Introductionmentioning

confidence: 99%

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Phase transitions in a system of hard rectangles on the square lattice

Kundu

Rajesh

2014

Phys. Rev. E

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The phase diagram of a system of monodispersed hard rectangles of size m×mk on a square lattice is numerically determined for m = 2, 3 and aspect ratio k = 1, 2, . . . , 7. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solid-like phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large k are determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger m and k, showing that for k ≥ 7, the system undergoes three entropy driven phase transitions with increasing density. The nature of the different phase transitions are established and the critical exponents for the continuous transitions are determined using finite size scaling.

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Section: A Phase Diagrammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase transitions in a system of hard rectangles on the square lattice

Kundu

Rajesh

2014

Phys. Rev. E

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“…Recent work estimating the critical exponents may be found in Refs. [34,50,74,75]. For higher values of k, the number of symmetric high-density ordered states are 10 (3-NN), 8 (4-NN), and 6 (5-NN).…”

Section: Introductionmentioning

confidence: 99%

Multiple phase transitions in extended hard-core lattice gas models in two dimensions

Nath

Rajesh

2014

Phys. Rev. E

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We study the k-NN hard-core lattice gas model in which the first k next-nearest-neighbor sites of a particle are excluded from occupation by other particles on a two-dimensional square lattice. This model is the lattice version of the hard-disk system with increasing k corresponding to decreasing lattice spacing. While the hard-disk system is known to undergo a two-step freezing process with increasing density, the lattice model has been known to show only one transition. Here, based on Monte Carlo simulations and high-density expansions of the free energy and density, we argue that for k = 4,10,11,14,⋯, the lattice model undergoes multiple transitions with increasing density. Using Monte Carlo simulations, we confirm the same for k = 4,...,11. This, in turn, resolves an existing puzzle as to why the 4-NN model has a continuous transition against the expectation of a first-order transition.

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“…Second, restricting the lateral positions reduces computational effort. Third, lattice-models to investigate liquidcrystalline phase behaviour are well established in the literature, prominent examples being the Zwanzig model (involving discretised translational motion and discretised rotations) [33][34][35][36] and the Lebwohl-Lasher model (particles fixed to lattice sites, continuous rotational motion) [37][38][39]. These models have been successfully used to study orientational ordering both in bulk [37] and in spatially confined systems [34][35][36]38].…”

Section: Introductionmentioning

confidence: 99%

A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces

Kleppmann

Klapp

2015

The Journal of Chemical Physics

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Hybrid systems consisting of organic molecules at inorganic semiconductor surfaces are gaining increasing importance as thin film devices for optoelectronics. The efficiency of such devices strongly depends on the collective behavior of the adsorbed molecules. In the present paper we propose a novel, coarse-grained model addressing the condensed phases of a representative hybrid system, that is, para-sexiphenyl (6P) at zinc-oxide (ZnO). Within our model, intermolecular interactions are represented via a Gay-Berne potential (describing steric and van-der-Waals interactions) combined with the electrostatic potential between two linear quadrupoles. Similarly, the molecule-substrate interactions include a coupling between a linear molecular quadrupole to the electric field generated by the line charges characterizing ZnO(10-10). To validate our approach, we perform equilibrium Monte Carlo simulations, where the lateral positions are fixed to a 2D lattice, while the rotational degrees of freedom are continuous. We use these simulations to investigate orientational ordering in the condensed state. We reproduce various experimentally observed features such as the alignment of individual molecules with the line charges on the surface, the formation of a standing uniaxial phase with a herringbone structure, as well as the formation of a lying nematic phase.

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Lattice gas with nearest- and next-to-nearest-neighbor exclusion

Cited by 29 publications

References 35 publications

Phase transitions in a system of hard rectangles on the square lattice

Phase transitions in a system of hard rectangles on the square lattice

Multiple phase transitions in extended hard-core lattice gas models in two dimensions

A scale-bridging modeling approach for anisotropic organic molecules at patterned semiconductor surfaces

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