Head-tail asymmetry and ferroelectricity in uniaxial liquid crystals

Biscarini, Fabio; Zannoni, Claudio; Chiccoli, C.; Pasini, Paolo

doi:10.1080/00268979100101301

Cited by 69 publications

(45 citation statements)

References 32 publications

(54 reference statements)

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“…The long axes of the rotors are specified by the unit vectors σ i ), P 2 is the second-order Legendre polynomial, and J is a coupling parameter. The LL model has been intensively investigated using Monte Carlo techniques since its introduction [21,22,[24][25][26][27]35]. The most complete numerical analysis of the NI transition in the LL model using the conventional single spin flip Metropolis algorithm was carried out by Zhang et al [26] on systems up to a size of 28 3 .…”

Section: Simulations and Resultsmentioning

confidence: 99%

Disclination loop behavior near the nematic-isotropic transition

Priezjev

Pelcovits

2001

Phys. Rev. E

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We investigate the behavior of disclination loops in the vicinity of the first order nematic-isotropic transition in the Lebwohl-Lasher and related models. We find that two independent measures of the transition temperature, the free energy and the distribution of disclination line segments, give essentially identical values. We also calculate the distribution function D(p) of disclination loops of perimeter p and fit it to a quasiexponential form. Below the transition, D(p) falls off exponentially, while in the neighborhood of the transition it decays with a power law exponent approximately equal to 2.5, consistent with a "blowout" of loops at the transition. In a modified Lebwohl-Lasher model with a strongly first-order transition we are able to measure a jump in the disclination line tension at the transition, which is too small to be measured in the Lebwohl-Lasher model. We also measure the monopole charge of the disclination loops and find that in both the original and modified Lebwohl-Lasher models, there are large loops which carry monopole charge, while smaller isolated loops do not. Overall the nature of the topological defects in both models is very similar.

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Section: Simulations and Resultsmentioning

confidence: 99%

Disclination loop behavior near the nematic-isotropic transition

Priezjev

Pelcovits

2001

Phys. Rev. E

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“…This can then be minimised with respect to the order parameters to determine their temperature dependence from which the transition temperatures and phase map are estimated [27]. However, since there are nine order parameters and six intermolecular coefficients for this nematogen it is a formidable task.…”

Section: Molecular Field Theorymentioning

confidence: 99%

Molecular field theory for biaxial nematic liquid crystals composed of molecules withC2hpoint group symmetry

et al. 2011

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The biaxial nematic phase is generally taken, either explicitly or implicitly, to have D 2h point group symmetry. However, it is possible for the biaxial phase to have a lower symmetry depending on that of its constituent molecules. Here we develop a molecular field theory for a nematogen composed of C 2h molecules in terms of the nine independent second rank orientational order parameters defining the C 2h biaxial nematic. In addition there is a rank one order parameter constructed from two pseudovectors which is only non-zero in the C 2h phase. The theory is simplified by removing all but the three dominant order parameters. The predicted phase behaviour is found to be rich with three possible biaxial nematic phases and with the transitions involving a biaxial nematic phase exhibiting tricritical points.

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“…In addition, a mixed isovector/isotensor model generalizing the RP 2 theory has been proposed as a model of orientational transitions in crystals [35] and of uniaxial liquid crystals exhibiting various kinds of head-tail asymmetry [36,37,38]; and a mixed isovector/isotensor model generalizing the RP N −1 theory arose in a study of Ncomponent ferromagnets with annealed random couplings [39,40].…”

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confidence: 99%

Pathologies of the large-N limit for RPN−1, CPN−1, QPN−1 and mixed isovector/isotensor σ-models

Sokal¹,

Starinets²

2001

Nuclear Physics B

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We compute the phase diagram in the N → ∞ limit for lattice RP N −1 , CP N −1 and QP N −1 σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N = ∞ limit exhibits phase transitions that are forbidden for any finite N . We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N → ∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N -component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.

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Head-tail asymmetry and ferroelectricity in uniaxial liquid crystals

Cited by 69 publications

References 32 publications

Disclination loop behavior near the nematic-isotropic transition

Disclination loop behavior near the nematic-isotropic transition

Molecular field theory for biaxial nematic liquid crystals composed of molecules withC2hpoint group symmetry

Pathologies of the large-N limit for RPN−1, CPN−1, QPN−1 and mixed isovector/isotensor σ-models

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