Theory and simulation of two-dimensional nematic and tetratic phases

Geng, Jun; Selinger, Jonathan V.

doi:10.1103/physreve.80.011707

Cited by 43 publications

(41 citation statements)

References 14 publications

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“…with the rescaled excess free-energy density Φ( r), which features all phases that were observed by simulations [25][26][27]35 and experiments 60-62 for a fluid of hard rectangles, i.e., an isotropic, a nematic, a tetratic, and a smectic phase. An illustration of the different phases is given by Fig.…”

Section: Introductionmentioning

confidence: 82%

Liquid crystals of hard rectangles on flat and cylindrical manifolds

Sitta

Smallenburg

Wittkowski

et al. 2018

Phys. Chem. Chem. Phys.

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Using the classical density functional theory of freezing and Monte Carlo computer simulations, we explore the liquid-crystalline phase behavior of hard rectangles on flat and cylindrical manifolds. Moreover, we study the effect of a static external field which couples to the rectangles' orientations, aligning them towards a preferred direction. In the flat and field-free case, the bulk phase diagram involves stable isotropic, nematic, tetratic, and smectic phases depending on the aspect ratio and number density of the particles. The external field shifts the transition curves significantly and generates a binematic phase at the expense of the tetratic phase. On a cylindrical manifold, we observe tilted smectic-like order, as obtained by wrapping a smectic layer around a cylinder. We find in general good agreement between our density functional calculations and particle-resolved computer simulations and mention possible setups to verify our predictions in experiments.

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Section: Introductionmentioning

confidence: 82%

Liquid crystals of hard rectangles on flat and cylindrical manifolds

Sitta

Smallenburg

Wittkowski

et al. 2018

Phys. Chem. Chem. Phys.

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“…A related model, with a similar phase diagram, was also studied in Ref. [15]. An interesting question is whether, for q > 2, the topology of the phase diagram remains unchanged.…”

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confidence: 97%

New Ordered Phases in a Class of GeneralizedXYModels

2011

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It is well known that the 2d XY model exhibits an unusual infinite order phase transition belonging to the Kosterlitz-Thouless (KT) universality class. Introduction of a nematic coupling into the XY Hamiltonian leads to an additional phase transition in the Ising universality class [1]. In this paper, using a combination of extensive Monte Carlo simulations and finite size scaling, we show that the higher order harmonics lead to a qualitatively different phase diagram, with additional ordered phases originating from the competition between the ferromagnetic and pseudo-nematic couplings. The new phase transitions belong to the 2d Potts, Ising, or KT universality classes.The low temperature behavior of two dimensional (2d) systems with continuous symmetries is controlled by topological defects, such as vortices and domain walls. Although massless Goldstone excitations, such as spin waves, destroy the long-range order of these systems, a pseudo-long-range order with algebraically decaying correlation functions still remains possible. At low temperatures the topological defects which undermine the pseudo-long-range order are all paired up, while above the critical temperature these defects unbind, leading to exponentially decaying correlation functions and a loss of the pseudo-long-range order. A classical example of such system is the XY model. At low temperature, the topological defects, in the form of integer valued vortices, are all joined in vortex-antivortex pairs, resulting in algebraically decaying spin-spin correlation functions. Above the Kosterlitz-Thouless (KT) critical temperature [2,3], these pairs unbind and the correlation functions decay exponentially.Unlike in 3d, for 2d systems the arguments based purely on symmetry considerations are not sufficient to fix the universality class of possible phase transitions [4][5][6][7], and even in 3d a second order phase transition can be preempted by a first order one [8]. Violations of strong universality are even more common in 2d. Thus, it is possible for systems with the same underlying symmetries and the same coarse-grained Landau-GinzburgWilson Hamiltonian not to belong to the same universality class. It is, therefore, interesting to ask what phase transitions are possible for 2d Hamiltonians invariant under the transformation θ → θ + 2π. In this paper, we will study using extensive Monte Carlo simulations and finite size scaling (FSS) analysis, a large class of generalized XY models which, while preserving the same θ → θ+2π symmetry, have very complex phase diagrams, with phase transitions belonging to the Ising and Potts universality classes, in addition to the usual KT phase transition. In some of these models, transitions can be understood in terms of new topological defects, such as fractional vortices and domain walls [1,9]. Apart from the fundamental considerations regarding the connection between symmetry and universality, our purpose is to describe new, previously unnoticed, ordered phases which occur in 2d systems with continuous symmetry.The m...

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“…For L = 4, the above T (4) tensor can be copied ("folded") into a real, symmetric and traceless matrix of order 9, say H [40, 81,82], where, for example,…”

Section: Moreovermentioning

confidence: 99%

Computer simulation study of a mesogenic lattice model based on long-range dispersion interactions

Romano

2016

Phys. Rev. E

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In contrast to thermotropic biaxial nematic phases, for which some long sought for experimental realizations have been obtained, no experimental realizations are yet known for their tetrahedratic and cubatic counterparts, involving orientational orders of ranks 3 and 4, respectively, also studied theoretically over the last few decades. In previous studies, cubatic order has been found for hard-core or continuous models consisting of particles possessing cubic or nearly-cubic tetragonal or orthorhombic symmetries; in a few cases, hard-core models involving uniaxial (D ∞h −symmetric) particles have been claimed to produce cubatic order as well. Here we address by Monte Carlo simulation a lattice model consisting of uniaxial particles coupled by long-range dispersion interactions of the London-De Boer-Heller type; the model was found to produce no second-rank nematic but only fourth-rank cubatic order, in contrast to the nematic behavior long known for its counterpart with interactions truncated at nearest-neighbor separation.

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Theory and simulation of two-dimensional nematic and tetratic phases

Cited by 43 publications

References 14 publications

Liquid crystals of hard rectangles on flat and cylindrical manifolds

Liquid crystals of hard rectangles on flat and cylindrical manifolds

New Ordered Phases in a Class of GeneralizedXYModels

Computer simulation study of a mesogenic lattice model based on long-range dispersion interactions

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