Thermal Fluctuations in a Lamellar Phase of a Binary Amphiphile-Solvent Mixture: A Molecular Dynamics Study

We investigate thermal fluctuations in a smectic A phase of an amphiphile-solvent mixture with molecular dynamics simulations. We use an idealized model system, where solvent particles are represented by simple beads, and amphiphiles by bead-and-spring tetramers. At a solvent bead fraction of 20 % and sufficiently low temperature, the amphiphiles self-assemble into a highly oriented lamellar phase. Our study aims at comparing the structure of this phase with the predictions of the elastic theory of thermally fluctuating fluid membrane stacks [Lei et al., J. Phys. II 5, 1155 (1995)]. We suggest a method which permits to calculate the bending rigidity and compressibility modulus of the lamellar stack from the simulation data. The simulation results are in reasonable agreement with the theory

Relative Chirality Of Octupolar Columns In A Triangular Array

The relative chirality of helical columns of planar disks having threefold symmetry,is studied using a model Hamiltonian derived from symmetry arguments that describe low-order octupole interactions. The columns are assumed to pack in a triangular array perpendicular to the columnar axes. Ground-state and finite-temperature mean-field phase diagrams are obtained as functions of interaction parameters. Due to the structure of the disks, there appears a term in the Hamiltonian that is not present for systems with lower internal symmetry, such as classical spin systems. This interaction is responsible for the stabilization of phases in which one third of the columns have a chirality opposite to the others. Such a phase has been observed in the discotic liquid crystal hexa-hexylthiotriphenylene

Smectic order, pinning, and phase transition in a smectic liquid crystal cell with a random substrate

We study smectic-liquid-crystal order in a cell with a heterogeneous substrate imposing surface random positional and orientational pinnings. Proposing a minimal random elastic model, we demonstrate that, for a thick cell, the smectic state without a rubbed substrate is always unstable at long scales and, for weak random pinning, is replaced by a smectic glass state. We compute the statistics of the associated substrate-driven distortions and the characteristic smectic domain size on the heterogeneous substrate and in the bulk. We find that for weak disorder, the system exhibits a three-dimensional temperature-controlled phase transition between a weakly and strongly pinned smectic glass states akin to the Cardy-Ostlund phase transition. We explore experimental implications of the predicted phenomenology and suggest that it provides a plausible explanation for the experimental observations on polarized light microscopy and x-ray scattering.Comment: 30 pages, 11 figures, Published in PRE, with minor typos correcte

Thermal phase diagrams of columnar liquid crystals

In order to understand the possible sequence of transitions from the disordered columnar phase to the helical phase in hexa(hexylthio)triphenylene (HHTT), we study a three-dimensional planar model with octupolar interactions inscribed on a triangular lattice of columns. We obtain thermal phase diagrams using a mean-field approximation and Monte Carlo simulations. These two approaches give similar results, namely, in the quasi one-dimensional regime, as the temperature is lowered, the columns order with a linear polarization, whereas helical phases develop at lower temperatures. The helicity patterns of the helical phases are determined by the exact nature of the frustration in the system, itself related to the octupolar nature of the molecules.Comment: 12 pages, 9 figures, ReVTe

The Smectic AA-CC Phase Transition in Biaxial Disordered Environments

We study the smectic $A$-$C$ phase transition in biaxial disordered environments, e.g. fully anisotropic aerogel. We find that both the $A$ and $C$ phases belong to the universality class of the "XY Bragg glass", and therefore have quasi-long-ranged translational smectic order. The phase transition itself belongs to a new universality class, which we study using an $\epsilon=7/2-d$ expansion. We find a stable fixed point, which implies a continuous transition, the critical exponents of which we calculate

First order isotropic - smectic-A transition in liquid crystal-aerosil gels

The short-range order which remains when the isotropic to smectic-A transition is perturbed by a gel of silica nanoparticles (aerosils) has been studied using high-resolution synchrotron x-ray diffraction. The gels have been created \textit{in situ} in decylcyanobiphenyl (10CB), which has a strongly first-order isotropic to smectic-A transition. The effects are determined by detailed analysis of the temperature and gel density dependence of the smectic structure factor. In previous studies of the continuous nematic to smectic-A transition in a variety of thermotropic liquid crystals the aerosil gel appeared to pin, at random, the phase of the smectic density modulation. For the isotropic to smectic-A transition the same gel perturbation yields different results. The smectic correlation length decreases more slowly with increasing random field variance in good quantitative agreement with the effect of a random pinning field at a transition from a uniform phase directly to a phase with one-dimensional translational order. We thus compare the influence of random fields on a \textit{freezing} transition with and without an intervening orientationally ordered phase.Comment: 8 pages, 8 figure

Histogram Monte Carlo study of multicritical behavior in the hexagonal easy-axis Heisenberg antiferromagnet

The results of a detailed histogram Monte-Carlo study of critical-fluctuation effects on the magnetic-field temperature phase diagram associated with the hexagonal Heisenberg antiferromagnet with weak axial anisotropy are reported. The multiphase point where three lines of continuous transitions merge at the spin-flop boundary exhibits a structure consistent with scaling theory but without the usual umbilicus as found in the case of a bicritical point.Comment: 7 pages (RevTex 3.0), 1 figure available upon request, CRPS-93-1

Fluctuations and phase transitions in Larkin-Ovchinnikov liquid crystal states of population-imbalanced resonant Fermi gas

Motivated by a realization of imbalanced Feshbach-resonant atomic Fermi gases, we formulate a low-energy theory of the Fulde-Ferrell and the Larkin-Ovchinnikov (LO) states and use it to analyze fluctuations, stability, and phase transitions in these enigmatic finite momentum-paired superfluids. Focusing on the unidirectional LO pair-density wave state, that spontaneously breaks the continuous rotational and translational symmetries, we show that it is characterized by two Goldstone modes, corresponding to a superfluid phase and a smectic phonon. Because of the liquid-crystalline "softness" of the latter, at finite temperature the 3d state is characterized by a vanishing LO order parameter, quasi-Bragg peaks in the structure and momentum distribution functions, and a "charge"-4, paired Cooper-pairs, off-diagonal-long-range order, with a superfluid-stiffness anisotropy that diverges near a transition into a nonsuperfluid state. In addition to conventional integer vortices and dislocations the LO superfluid smectic exhibits composite half-integer vortex-dislocation defects. A proliferation of defects leads to a rich variety of descendant states, such as the "charge"-4 superfluid and Fermi-liquid nematics and topologically ordered nonsuperfluid states, that generically intervene between the LO state and the conventional superfluid and the polarized Fermi-liquid at low and high imbalance, respectively. The fermionic sector of the LO gapless superconductor is also quite unique, exhibiting a Fermi surface of Bogoliubov quasiparticles associated with the Andreev band of states, localized on the array of the LO domain-walls.Comment: 56 pages, 21 figure

Magnetic-Field Induced First-Order Transition in the Frustrated XY Model on a Stacked Triangular Lattice

The results of extensive Monte Carlo simulations of magnetic-field induced transitions in the xy model on a stacked triangular lattice with antiferromagnetic intraplane and ferromagnetic interplane interactions are discussed. A low-field transition from the paramagnetic to a 3-state (Potts) phase is found to be very weakly first order with behavior suggesting tricriticality at zero field. In addition to clarifying some long-standing ambiguity concerning the nature of this Potts-like transition, the present work also serves to further our understanding of the critical behavior at $T_N$, about which there has been much controversy.Comment: 10 pages (RevTex 3.0), 4 figures available upon request, CRPS-93-0

Magnetic Phase Diagram of the Ferromagnetically Stacked Triangular XY Antiferromagnet: A Finite-Size Scaling Study

Histogram Monte-Carlo simulation results are presented for the magnetic-field -- temperature phase diagram of the XY model on a stacked triangular lattice with antiferromagnetic intraplane and ferromagnetic interplane interactions. Finite-size scaling results at the various transition boundaries are consistent with expectations based on symmetry arguments. Although a molecular-field treatment of the Hamiltonian fails to reproduce the correct structure for the phase diagram, it is demonstrated that a phenomenological Landau-type free-energy model contains all the esstential features. These results serve to complement and extend our earlier work [Phys. Rev. B {\bf 48}, 3840 (1993)].Comment: 5 pages (RevTex 3.0), 6 figures available upon request, CRPS 93-