Liquid polymorphism and density anomaly in a three-dimensional   associating lattice gas
  We investigate the phase diagram of a three-dimensional associating gas $(ALG)$ model. This model combines orientational ice-like interactions and ``van der Waals'' that might be repulsive, representing, in this case, a penalty for distortion of hydrogen bonds. These interactions can be interpreted as two competing distances making the connection between this model and continuous isotropic soft-core potentials. We present Monte Carlo studies of the $ALG$ model showing the presence of two liquid phase, two critical points and A density anomaly. 
Mauricio Girardi, Aline L. Balladares, Vera B. Henriques, Marcia C.   Barbosa