Liquid Crystal Lattice Models on Quadrics Supercomputers

Boschi, Sigismondo; Brunelli, Marco P.; Zannoni, Claudio; Chiccoli, C.; Pasini, Paolo

doi:10.1142/s0129183197000436

Cited by 8 publications

(5 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Simulations and Resultsmentioning

confidence: 99%

Disclination loop behavior near the nematic-isotropic transition

Priezjev

Pelcovits

2001

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…We also take 0.5(U * 3 Õ U * 1 ) as a crude estimate of the energy jump at the phase transition. As a rough estimate for the order parameters at the nematic± isotropic transition P ± NI 2 and P ± NI 4 , we propose For comparison, we also give here simulation estimates for the transitional properties of the Lebwohl± Lasher model, obtained by other authors and for q carried out with q = 120 has been published [40] ); fME, 4 , see equation (51), hardly distinguishable from the T * NI = 1.1232Ô 0.0001 [28, 32, 41± 43] ; DU * NI = 0.20Ô 0.04 continuous one. The relative statistical errors on the and hence D S NI / R = 0 .18 Ô 0.04 [42] ; notice that [32] simulation results range up to 0.2%.…”

Section: Results and Comparisonsmentioning

confidence: 99%

Computer simulation study of a nematogenic lattice model based on an elastic energy mapping of the pair potential

Luckhurst¹,

Romano²

1999

Liquid Crystals

View full text Add to dashboard Cite

Director con® gurations in a nematic liquid crystal can be determined by minimizing its total elastic free energy, for given elastic constants and speci® c boundary conditions. In some cases, these con® gurations have been obtained by numerical procedures where the elastic free energy density plays the same role as the overall potential energy in a standard Metropolis Monte Carlo simulation. The interaction energies or potentials used in these studies are short ranged but, in general, not pairwise additive, unless the three elastic constants are set to a common value, thus reducing the potential to that in the well-known Lebwohl± Lasher lattice model. On the other hand, we can construct, in di erent ways, a lattice model with pairwise additive interactions, which approximately reproduces the elastic free energy density, where the parameters de® ning the pair potential are expressed as linear combinations of elastic constants. An anisotropic nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess (T. Gruhn and S. Hess, Z. Naturforsch. A51, 1 (1996)), has recently been investigated by one of us, using a Monte Carlo simulation (S. Romano, Int. J. Mod. Phys. B 12, 2305(1998).Here we propose another approximate procedure for the mapping, and study the resulting pair potential model with the aid of Monte Carlo simulations. The behaviour of the nematic phases formed by the two models is compared together with the predictions of molecular ® eld theory and the properties of the Lebwohl± Lasher model.

show abstract

“…where the sum is over all nearest-neighbors and ǫ is a coupling parameter. The LL model has been intensively investigated using Monte Carlo techniques since its introduction [2][3][4][5][6][7].…”

mentioning

confidence: 99%

“…In a Monte Carlo simulation the system gets trapped in one of the free energy wells corresponding to the nematic or isotropic phase, and the conventional single flip Metropolis algorithm becomes inefficient especially as the system size is increased. While Boschi et al [7] carried out simulations on systems as large as 120 × 120 × 120, the most detailed study of the NI transition was carried out by Zhang et al [6] on systems up to 28×28×28. These authors used the Lee-Kosterlitz finite size scaling method [8,9], supplemented by the Ferrenberg-Swendsen reweighting technique [10] to determine the order of the NI transitions and estimate the value of the transition temperature T c in the thermodynamic limit.…”

mentioning

confidence: 99%

Cluster Monte Carlo simulations of the nematic-isotropic transition

Priezjev

Pelcovits

2001

Phys. Rev. E

View full text Add to dashboard Cite

We report the results of simulations of the three-dimensional Lebwohl-Lasher model of the nematic-isotropic transition using a single cluster Monte Carlo algorithm. The algorithm, first introduced by Kunz and Zumbach to study two-dimensional nematics, is a modification of the Wolff algorithm for spin systems, and greatly reduces critical slowing down. We calculate the free energy in the neighborhood of the transition for systems up to linear size 70. We find a double well structure with a barrier that grows with increasing system size. We thus obtain an upper estimate of the value of the transition temperature in the thermodynamic limit.

show abstract

Liquid Crystal Lattice Models on Quadrics Supercomputers

Cited by 8 publications

References 10 publications

Disclination loop behavior near the nematic-isotropic transition

Disclination loop behavior near the nematic-isotropic transition

Computer simulation study of a nematogenic lattice model based on an elastic energy mapping of the pair potential

Cluster Monte Carlo simulations of the nematic-isotropic transition

Contact Info

Product

Resources

About