  Four scenarios have been proposed for the low--temperature phase behavior of
liquid water, each predicting different thermodynamics. The physical mechanism
which leads to each is debated. Moreover, it is still unclear which of the
scenarios best describes water, as there is no definitive experimental test.
Here we address both open issues within the framework of a microscopic cell
model by performing a study combining mean field calculations and Monte Carlo
simulations. We show that a common physical mechanism underlies each of the
four scenarios, and that two key physical quantities determine which of the
four scenarios describes water: (i) the strength of the directional component
of the hydrogen bond and (ii) the strength of the cooperative component of the
hydrogen bond. The four scenarios may be mapped in the space of these two
quantities. We argue that our conclusions are model-independent. Using
estimates from experimental data for H bond properties the model predicts that
the low-temperature phase diagram of water exhibits a liquid--liquid critical
point at positive pressure.
