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. (Some figures in this article are in colour only in the electronic version)