By the 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 allows us to study the water thermodynamic behavior 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.