We analyze the ground states and the elementary collective excitations (phonons) of a class of systems, which form cluster crystals in the absence of attractions. Whereas the regime of moderate-to-high temperatures in the phase diagram has been analyzed in detail by means of density functional considerations (Likos et al 2007 J. Chem. Phys. 126 224502), the present approach focuses on the complementary regime of low temperatures. We establish the existence of an infinite cascade of isostructural transitions between crystals with different lattice site occupancies at T = 0 and we quantitatively demonstrate that the thermodynamic instabilities are bracketed by mechanical instabilities arising from long-wavelength acoustical phonons. We further show that all optical modes are degenerate and flat, giving rise to almost perfect realizations of Einstein crystals. We calculate analytically the complete phonon spectrum for the whole class of models as well as the Helmholtz free energy of the systems. On the basis of the latter, we demonstrate that the aforementioned isostructural phase transitions must terminate at an infinity of critical points at low temperatures, brought about by the anharmonic contributions in the Hamiltonian and the hopping events in the crystals.

When a fluid with a bulk liquid-vapor critical point is placed inside a static external field with spatial periodic oscillations in one direction, a new phase arises. This new phase-the so-called "zebra" phase-is characterized by an average density roughly between that of the liquid and vapor phases. The presence of the zebra phase gives rise to two new phase transitions: one from the vapor to the zebra phase, and one from the zebra to the liquid phase. At appropriate values of the temperature and chemical potential, the latter two transitions become critical. This phenomenon is called laser-induced condensation [I. O. Götze, J. M. Brader, M. Schmidt, and H. Löwen, Mol. Phys. 101, 1651 (2003)]. The purpose of this paper is to elucidate the nature of the critical points, using density functional theory and computer simulation of a colloid-polymer mixture. The main finding is that critical correlations develop in two-dimensional sheets perpendicular to the field direction, but not in the direction along the field: the critical correlations are thus effectively two-dimensional. Hence, static periodic fields provide a means to confine a fluid to effectively two dimensions. Away from criticality, the vapor-zebra and liquid-zebra transitions become first-order, but the associated surface tensions are extremely small. The consequences of the extremely small surface tensions on the nature of the two-phase coexistence regions are analyzed in detail.

A competition of incommensurate symmetries occurs whenever a system is forced to conform to an ordering that is different from the intrinsically preferred structure of the system itself. As a model system of such a competition, we study the rivalry between the triangular ordering of hard disks and the square symmetry induced by a periodic square substrate. By using density functional theory as well as Monte Carlo computer simulations, we determine the full phase behavior for the case of one particle per minimum. We observe a rhombic preordering structure preceding the hexagonal solid as a direct consequence of the competing symmetries. Furthermore, the square-rhombic transition is reentrant with increasing substrate interaction. Our predictions can be verified in experiments of colloids in laser fields.

We explore the crystallization in a colloidal monolayer on a structured template starting from a few-particle nucleus. The competition between the substrate structure and that of the growing crystal induces a new crystal growth scenario. Unlike with the crystal growth in the bulk where a welldefined and connected crystal-fluid interface grows into the fluid, we identify a mechanism where a 'compatibility wave' of the prescribed nucleus with the underlying substrate structure dictates the growth direction and efficiency. The growth process is strongly anisotropic and proceeds via transient island formation in front of an initial solid-fluid interface. We demonstrate the validity of this compatibility wave concept for a large class of substrate structures including a square lattice and a quasicrystalline pattern. Dynamical density functional theory that provides a microscopic approach to the crystallization process is employed for colloidal hard spheres. Our predictions can be verified in experiments on confined colloids and also bear consequences for molecular crystal growth on structured substrates.

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