Monte Carlo simulations herringbone ordering

Several N2-N2 intermolecular potentials were examined with respect to their herringbone transition temperature under otherwise identical conditions based on canonical Monte Carlo simulations with 900 classical N2 molecules [217]. The simulations were performed in strictly two dimensions and the centers of mass were fixed on a triangular lattice. No finite-size extrapolations whatsoever were performed so that the transition temperatures obtained from the heat capacity maxima are only of a qualitative nature. The N2-graphite interaction was modeled by the first-order Fourier expansion technique [324, 326, 327] and is included only for the realistic atom-atom... 

The first Monte Carlo simulation [244] (see also the broad discussion in Section 5.3 of Ref. 246) focusing on the order of the herringbone transition was based on the strictly two-dimensional anisotropic-planar-rotor model (2.5), which is similar to the planar model used in Ref. 274 except that the quadrupole interactions are treated only approximately (see Section II.B for forther details). The instrument of diagnostics was the three-component herringbone order parameter [244, 246] defined as... 

Figure 33. Herringbone orientational correlation functions F (3.15) in the inset and the logarithmic derivatives 62 In (3.18) as a function of distance I in units of the lattice constant a - 4.26 A in the disordered phase of the anisotropic-planar-rotor model (2.5) from Monte Carlo simulations at 7" = 25.5 K and a linear system size of L = 180. The different symbols distinguish the three symmetty axes a, and the dashed line marks the plateau 2/. In the inset all three F fall on top of each other and the different symbols denote here the two oscillating parts of the antiferromagnetic-like ordering pattern. (Adapted from Fig. 1 of Ref. 273.)...

Figure 38. Striped domain wall in a model of uniaxially compressed N2 monolayers on graphite (a) observed in Monte Carlo simulations of 52 X 12 molecules at 10 K and a coverage of 1.026 monolayers. Dots denote the centers of the honeycomb hexagons of the graphite basal plane, and crosses mark the mean positions of the molecular centers of mass. The inset of (a) shows the herringbone order in the commensurate region at the left and right boundaries of (a). The center-of-mass distribution in the region of the domain wall of (a) sampled from the Monte Carlo trajectory is magnified in (b). (Adapted from Fig. 1 of Ref. 283.)...

Using Monte-Carlo simulations, we have investigated the role of herringbone order on the liquid-hexatic transition of nmOBC [42]. Based on the coupled XY Hamilton-... 

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