  Strongly anchored free-standing smectic films usually present a stepwise
reduction of the number of layers when the temperature is raised above the
smectic-isotropic bulk transition temperature. Here, we demonstrate that a
field-induced layer thinning transition can take place in smectic films with a
negative dielectric anisotropy even below the bulk transition temperature.
Using an extended McMillan's model, we provide the phase diagram of this
layering transition and show that, when the field is raised above the bulk
transition field, the film thickness reduction is well described by a power-law
with an exponent that depends on the temperature and the aspect ratio of the
liquid crystal molecule.
