Liquid polyamorphism and double criticality in a lattice gas model

We analyse the possible phase diagrams of a simple model for an associating liquid proposed previously. Our two-dimensional lattice model combines orientational ice-like interactions and 'van der Waals' interactions which may be repulsive, and in this case represent a penalty for distortion of hydrogen bonds in the presence of extra molecules. These interactions can be interpreted in terms of two competing distances, but not necessarily soft-core. We present mean-field calculations and an exhaustive simulation study for different parameters which represent the relative strength of the bonding interaction to the energy penalty for its distortion. As this ratio decreases, a smooth disappearance of the double criticality occurs. Possible connections to liquid-liquid transitions of molecular liquids are suggested.