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The liquid-liquid critical point scenario of water hypothesizes the existenceof two metastable liquid phases---low-density liquid (LDL) and high-densityliquid (HDL)---deep within the supercooled region. The hypothesis originatesfrom computer simulations of the ST2 water model, but the stability of the LDLphase with respect to the crystal is still being debated. We simulatesupercooled ST2 water at constant pressure, constant temperature and constantnumber of molecules N for N<=729 and times up to 1000 ns. We observe cleardifferences between the two liquids, both structural and dynamical. Usingseveral methods, including finite-size scaling, we confirm the presence of aliquid-liquid phase transition ending in a critical point. We find that the LDLis stable with respect to the crystal in 98% of our runs (we perform 372 runsfor LDL or LDL-like states), and in 100% of our runs for the two largest systemsizes (N=512 and 729, for which we perform 136 runs for LDL or LDL-likestates). In all these runs tiny crystallites grow and then melt within 1000 ns.Only for N<=343 we observe six events (over 236 runs for LDL or LDL-likestates) of spontaneous crystallization after crystallites reach an estimatedcritical size of about 70+/-10 molecules.

Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization