Importance of many-body orientational correlations in the physical description of liquids.

Liquids are often assumed to be homogeneous and isotropic at any lengthscale and translationally invariant. The standard liquid-state theory is constructed on the basis of this picture and thus basically described in terms of the two-body density correlation. This picture is certainly valid at rather high temperatures, where a liquid is in a highly disordered state. However, it may not necessarily be valid at low temperatures or for a system which has strong directional bonding. Indeed, there remain fundamental unsolved problems in liquid science, which are difficult to explain by such a theory. They include water's thermodynamic and kinetic anomalies, liquid-liquid transitions, liquid-glass transitions, and liquid-solid transitions. We argue that for the physical description of these phenomena it is crucial to take into account many-body (orientational) correlations, which have been overlooked in the conventional liquid-state theory. It is essential to recognise that a liquid can lower its free energy by local or mesoscopic ordering without breaking global symmetry. Since such ordering must involve at least a central particle and its neighbours, which are more than two particles, it is intrinsically a consequence of many-body correlations. Particularly important ordering is associated with local breakdown of rotational symmetry, i.e., bond orientational ordering. We emphasize that translational ordering is global whereas orientational ordering can be local. Because of the strong first-order nature of translational ordering, its growth in a liquid state is modest. Thus any structural ordering in a liquid should be associated primarily with orientational ordering and not with translational ordering. We show that bond orientational ordering indeed plays a significant role in all the above-mentioned phenomena at least for (quasi-)single-component liquids. In this Introductory Lecture, we discuss how these phenomena can be explained by such local or mesoscopic ordering in a unified manner.