  In a previous paper [J. Chem. Phys. 129, 024506 (2008)] we studied a 3
dimensional lattice model of a network-forming fluid, recently proposed in
order to investigate water anomalies. Our semi-analytical calculation, based on
a cluster-variation technique, turned out to reproduce almost quantitatively
several Monte Carlo results and allowed us to clarify the structure of the
phase diagram, including different kinds of orientationally ordered phases.
Here, we extend the calculation to different parameter values and to other
similar models, known in the literature. We observe that analogous ordered
phases occur in all these models. Moreover, we show that certain "waterlike"
thermodynamic anomalies, claimed by previous studies, are indeed artifacts of a
homogeneity assumption made in the analytical treatment. We argue that such a
difficulty is common to a whole class of lattice models for water, and suggest
a possible way to overcome the problem.
