We have determined the phase diagram for a lattice system of biaxial particles interacting with a second rank anisotropic potential using Monte Carlo simulations for a number of values of the molecular biaxiality. We find increasing differences from mean field theory as the biaxiality increases. We have also calculated for the first time the full set of second rank biaxial and uniaxial order parameters and their temperature dependence, and on this basis we comment on the difficulties of measuring phase biaxiality by NMR.
It is now generally accepted that even low amounts of quenched disorder disrupt long-range order in anisotropic systems with continuous symmetry. However, very little is known on the key item of the nature of the residual order, if any, and particularly if this has quasi-long-range or truly-short-range character. Here we address this problem both experimentally for the nematic 6CB in dilute aerosils and with computer simulations. We find that the residual order is short ranged and scales with disorder density in agreement with the Imry-Ma argument.
Monte Carlo and theoretical studies of thin 3D films of biaxial and uniaxial nematics with tangential boundary conditions show distinct differences in structure and evolution of topological defects. In the uniaxial films, defects of strength k=+/-1 are point defects that bear no bulk singularity and disappear by annihilation with each other. In the biaxial films, k=+/-1 defects are true singular bulk disclinations that split into pairs of k=+/-1/2 lines; the latter disappear by annihilation processes of the type +1/2-1/2=0. These observed differences are of relevance for the current debate on the existence of biaxial phases.
Nematics with quenched disorder have been repeatedly predicted to form glass phases. Here we present turbidity experiments and computer simulations aimed at studying glass key features such as dynamics and history dependence in randomly perturbed nematics. Electric field-cooling alignment has been employed to prepare samples in suitably oriented starting states. Remarkable remnant order and slow dynamics are found both by experiment and simulations, indicating that random disorder can, by itself, induce a nematic glass state even without perturber restructuring.
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