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We investigate a minimal model for non-crystalline water, defined on a Husimilattice. The peculiar random-regular nature of the lattice is meant to accountfor the formation of a random 4-coordinated hydrogen-bond network. The modelturns out to be consistent with most thermodynamic anomalies observed in liquidand supercooled-liquid water. Furthermore, the model exhibits two glassy phaseswith different densities, which can coexist at a first-order transition. Theonset of a complex free-energy landscape, characterized by an exponentiallylarge number of metastable minima, is pointed out by the cavity method, at thelevel of 1-step replica symmetry breaking.

A discrete model of water with two distinct glassy phases