  We study the phase diagram of a system of spherical particles interacting in
three dimensions through a potential consisting of a strict hard core plus a
linear repulsive shoulder at larger distances. The phase diagram (obtained
numerically, and analytically in a limiting case) shows anomalous properties
that are similar to those observed in water. Specifically, we find maxima of
density and isothermal compressibility as a function of temperature, melting
with volume contraction, and multiple stable crystalline structures. If in
addition a long range attraction between the particles is included, the usual
liquid-gas coexistence curve with its critical point is obtained. But more
interestingly, a first order line in the metastable fluid branch of the phase
diagram appears, ending in a new critical point, as it was suggested to occur
in water. In this way the model provides a comprehensive, consistent and
unified picture of most of the anomalous thermodynamical properties of water,
showing that all of them can be qualitatively explained by the existence of two
competing equilibrium values for the interparticle distance.
