  We investigate a lattice-fluid model of water, defined on a three-dimensional
body centered cubic lattice. Model molecules possess a tetrahedral symmetry,
with four equivalent bonding arms, aiming to mimic the formation of hydrogen
bonds. The model is similar to the one proposed by Roberts and Debenedetti [J.
Chem. Phys. 105, 658 (1996)], simplified in that no distinction between bond
"donors" and "acceptors" is imposed. Bond formation depends both on orientation
and local density. In the ground state, we show that two different ordered
(ice) phases are allowed. At finite temperature, we analyze homogeneous phases
only, working out phase diagram, response functions, the temperature of maximum
density locus, and the Kauzmann line. We make use of a generalized first order
approximation on a tetrahedral cluster. In the liquid phase, the model exhibits
several anomalous properties observed in real water. In the low temperature
region (supercooled liquid), there are evidences of a second critical point
and, for some range of parameter values, this scenario is compatible with the
existence of a reentrant spinodal.
