  The properties of water can have a strong dependence on the confinement.
Here, we consider a water monolayer nanoconfined between hydrophobic parallel
walls under conditions that prevent its crystallization. We investigate, by
simulations of a many-body coarse-grained water model, how the properties of
the liquid are affected by the confinement. We show, by studying the response
functions and the correlation length and by performing finite-size scaling of
the appropriate order parameter, that at low temperature the monolayer
undergoes a liquid-liquid phase transition ending in a critical point in the
universality class of the two-dimensional (2D) Ising model. Surprisingly, by
reducing the linear size L of the walls, keeping the walls separation h
constant, we find a 2D-3D crossover for the universality class of the
liquid-liquid critical point for L/h~50, i.e. for a monolayer thickness that is
small compared to its extension. This result is drastically different from what
is reported for simple liquids, where the crossover occurs for L/h ~ 5, and is
consistent with experimental results and atomistic simulations. We shed light
on these findings showing that they are a consequence of the strong
cooperativity and the low coordination number of the hydrogen bond network that
characterizes water.
