  This paper extends our earlier studies of free energy functions of density
and crystalline order parameters for models of supercooled water, which allows
us to examine the possibility of two distinct metastable liquid phases [J.
Chem. Phys. 135, 134503 (2011) and arXiv:1107.0337v2]. Low-temperature
reversible free energy surfaces of several different atomistic models are
computed: mW water, TIP4P/2005 water, SW silicon and ST2 water, the last of
these comparing three different treatments of long-ranged forces. In each case,
we show that there is one stable or metastable liquid phase, and there is an
ice-like crystal phase. The time scales for crystallization in these systems
far exceed those of structural relaxation in the supercooled metastable liquid.
We show how this wide separation in time scales produces an illusion of a
low-temperature liquid-liquid transition. The phenomenon suggesting
metastability of two distinct liquid phases is actually coarsening of the
ordered ice-like phase, which we elucidate using both analytical theory and
computer simulation. For the latter, we describe robust methods for computing
reversible free energy surfaces, and we consider effects of electrostatic
boundary conditions. We show that sensible alterations of models and boundary
conditions produce no qualitative changes in low-temperature phase behaviors of
these systems, only marginal changes in equations of state. On the other hand,
we show that altering sampling time scales can produce large and qualitative
nonequilibrium effects. Recent reports of evidence of a liquid-liquid critical
point in computer simulations of supercooled water are considered in this
light.
