Liquid-liquid critical point in a Hamiltonian model for water: analytic solution

Water is characterized by a density anomaly whose origin is a matter of debate. Theoretical works have shown that two of the proposed explanations, the second-critical-point hypothesis and the singularity-free scenario, have the same microscopic origin, but arise from different choices of parameters, such as the hydrogen bond strength or geometry. We consider a Hamiltonian model proposed by Sastry et al that supports the singularity-free scenario and was solved in an approximation where the intra-molecular interactions are neglected. We show that, by including these interactions, the second critical point is recovered, elucidating the differences in the mechanisms at the origin of the two interpretations.