  Achieving a coherent understanding of the many thermodynamic and dynamic
anomalies of water is among the most important unsolved puzzles in physics,
chemistry, and biology. One hypothesized explanation imagines the existence of
a line of first order phase transitions separating two liquid phases and
terminating at a novel "liquid-liquid" critical point in a region of low
temperature ($T \approx 250 \rm{K}$) and high pressure ($P \approx 200
\rm{MPa}$). Here we analyze a common model of water, the ST2 model, and find
that the entire system flips between liquid states of high and low density.
Further, we find that in the critical region crystallites melt on a time scale
of nanoseconds. We perform a finite-size scaling analysis that accurately
locates both the liquid-liquid coexistence line and its associated
liquid-liquid critical point.
