  Understanding the wetting properties of premelting films requires knowledge
of the film's equation of state, which is not usually available. Here we
calculate the disjoining pressure curve of premelting films, and perform a
detailed thermodynamic characterization of premelting behavior on ice. Analysis
of the density profiles reveals the signature of weak layering phenomena, from
one to two and from two to three water molecular layers. However, disjoining
pressure curves, which closely follow expectations from a renormalized mean
field liquid state theory, show that there are no layering phase transitions in
the thermodynamic sense along the sublimation line. Instead, we find that
transitions at mean field level are rounded due to capillary wave fluctuations.
We see signatures that true first order layering transitions could arise at low
temperatures, for pressures between the metastable line of water/vapor
coexistence and the sublimation line. The extrapolation of the disjoining
pressure curve above water vapor saturation displays a true first order phase
transition from a thin to a thick film consistent with experimental
observations.
