  We use molecular dynamics simulations in two dimensions to investigate the
possibility that a core-softened potential can reproduce static and dynamic
anomalies found experimentally in liquid water: (i) the increase in specific
volume upon cooling, (ii) the increase in isothermal compressibility upon
cooling, and (iii) the increase in the diffusion coefficient with pressure. We
relate these anomalies to the shape of the potential. We obtain the phase
diagram of the system and identify two solid phases: a square crystal (high
density phase), and a triangular crystal (low density phase). We also discuss
the relation between the anomalies observed and the polymorphism of the solid.
Finally, we compare the phase diagram of our model system with experimental
data, noting especially the line of temperatures of maximum density, line of
pressures of maximum diffusion constant, and line of temperatures of minimum
isothermal compressibility.
