  Liquid-liquid and liquid-vapor coexistence regions of various water models
were determined by MC simulations of isotherms of density fluctuation
restricted systems and by Gibbs ensemble MC simulations. All studied water
models show multiple liquid-liquid phase transitions in the supercooled region:
we observe two transitions of the TIP4P, TIP5P and SPCE model and three
transitions of the ST2 model. The location of these phase transitions with
respect to the liquid-vapor coexistence curve and the glass temperature is
highly sensitive to the water model and its implementation. We suggest, that
the apparent thermodynamic singularity of real liquid water in the supercooled
region at about 228 K is caused by an approach to the spinodal of the first
(lowest density) liquid-liquid phase transition. The well known density maximum
of liquid water at 277 K is related to the second liquid-liquid phase
transition, which is located at positive pressures with a critical point close
to the maximum. A possible order parameter and the universality class of
liquid-liquid phase transitions in one-component fluids is discussed.
