General view of a liquid-liquid phase transition.

We present a general view of a liquid-liquid phase transition, based on a simple physical picture that there is "cooperative medium-range bond ordering" for any liquids. Contrary to the common belief, we argue that liquid is not homogeneous and in any liquid there exist locally favored structures, which are frustrated with normal-liquid structures. The cooperative excitation of locally favored structures leads to a gas-liquid-like critical point of bond ordering. This picture naturally leads to the conclusion that liquid-liquid transition is not specific to special materials, but can in principle exist in any liquids. Our model suggests a new possibility that (i) even an ordinary molecular liquid can have a hidden liquid-liquid phase transition and (ii) it may be the origin of a second amorphous phase (e.g., "glacial phase") and critical-like, large-scale fluctuations ("Fischer clusters") observed in supercooled molecular liquids.