Using Wolff's cluster Monte Carlo simulations and numerical minimization within a mean field approach, we study the low temperature phase diagram of water, adopting a cell model that reproduces the known properties of water in its fluid phases. Both methods allow us to study the thermodynamic behavior of water at temperatures, where other numerical approaches – both Monte Carlo and molecular dynamics – are seriously hampered by the large increase of the correlation times. The cluster algorithm also allows us to emphasize that the liquid–liquid phase transition corresponds to the percolation transition of tetrahedrally ordered water molecules.