  We consider the liquid-vapor type phase transition for fluids confined within
spatially periodic external fields. For a fluid in d=3 dimensions, the periodic
field induces an additional phase, characterized by large density modulations
along the field direction. At the triple point, all three phases (modulated,
vapor, and liquid) coexist. At temperatures slightly above the triple point and
for low (high) values of the chemical potential, two-phase coexistence between
the modulated phase and the vapor (liquid) is observed. We study this
phenomenon using computer simulations and mean-field theory for the Ising
model. The theory shows that, in order for the modulated phase to arise, the
field wavelength must exceed a threshold value. We also find an extremely low
tension of the interface between the modulated phase and the vapor/liquid
phases. The tension is of the order 10^{-4} kB T per squared lattice spacing,
where kB is the Boltzmann constant, and T the temperature. In order to detect
such low tensions, a new simulation method is proposed. We also consider the
case of d=2 dimensions. The modulated phase then does not survive, leading to a
radically different phase diagram.
