The phase behavior of a system composed of spherical particles with a monomodal size distribution is investigated theoretically within the context of the van der Waals approximation for polydisperse fluids. It is shown how the binodals, spinodals, cloud-point and shadow curves as well as all the (polydispersity induced) critical points can be obtained for a variety of interaction potentials. The polydispersity induced modifications of the phase diagram (even for a polydispersity index $I$ as small as $I\approx 1.01$) should be observable in some colloidal dispersions.Comment: 26 pages, 10 figure

We present Monte Carlo simulations of discotic molecules using the Gay-Berne potential with shape (kappa) and energy (kappa(')) anisotropies. Following the previous work of Bates and Luckhurst [J. Chem. Phys. 104, 6696 (1996)] at kappa=0.345, kappa(')=0.2 when we determine the sequence of different phases at the same reduced pressure P(*)=50, we find an additional phase at low temperatures corresponding to an orthorhombic crystalline phase and we characterize it. Keeping the shape anisotropy fixed at kappa=0.2, we determine the evolution of the phase diagram with varying energy anisotropy. At high kappa('), low anisotropy, the system is not able to build columns while at low kappa('), the system exhibits both orthorhombic crystal as well as hexagonal liquid crystal phases over a wide range of pressures and temperatures. The domain of stability of the nematic phase is found to systematically shift towards higher pressures as kappa(') decreases.

The classical Heisenberg antiferromagnet on the pyrochlore lattice is macroscopically and continuously degenerate and the system remains disordered at all temperatures, even in the presence of weak dilution with nonmagnetic ions. We show that, in stark contrast, weak bond disorder lifts the ground state degeneracy in favour of locally collinear spin configurations. We present a proof that for a single tetrahedron the ground state is perfectly collinear but identify two mechanisms which preclude the establishment of a globally collinear state; one due to frustration and the other due to higher-order effects. We thus obtain a rugged energy landscape, which is necessary to account for the glassy phenomena found in real systems such as the pyrochlore Y2Mo2O7 recently reported by Booth et al.[1] to contain a substantial degree of bond disorder.

We present Monte Carlo simulations of diskotic molecules using the Gay-Berne potential in a slab geometry. The disk-wall interaction is described by two different functions according to whether or not the equilibrium distance is dependent on the relative orientation of the disk to the wall. Furthermore, by changing the parameters of these potentials, we model either homeotropic (face-on) or planar (edge-on) anchoring of the disks. We have found that the isotropic-nematic transition does not change in comparison with the bulk situation. The temperature of the nematic-columnar transition, on the contrary, is found to increase for homeotropic anchoring, and decrease for planar anchoring, independently of the details of the potential. We explain the decrease of the transition temperature in the planar anchoring situation as the result of an induced frustration, due to the competition between the two orientations induced independently by the upper and lower walls.