Thermodynamic anomaly and polyamorphism of water

Here we present a simple model of water, focusing on hidden "medium-range ordering" in water. In addition to a density order parameter ρ, we need to introduce a bond order parameter S to represent the excitation of locally favored structures (medium-range ordering). Here we show that the excitation of S is described by a "two-state model with cooperative excitation". We propose that water's anomalies are "primarily" not due to critical phenomena, but a gas-liquid–like critical point of bond ordering may exist below the melting curve. These two facts are not inconsistent with each other but can be explained in a coherent manner.