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We consider the liquid-vapor type phase transition for fluids confined withinspatially periodic external fields. For a fluid in d=3 dimensions, the periodicfield induces an additional phase, characterized by large density modulationsalong the field direction. At the triple point, all three phases (modulated,vapor, and liquid) coexist. At temperatures slightly above the triple point andfor low (high) values of the chemical potential, two-phase coexistence betweenthe modulated phase and the vapor (liquid) is observed. We study thisphenomenon using computer simulations and mean-field theory for the Isingmodel. The theory shows that, in order for the modulated phase to arise, thefield wavelength must exceed a threshold value. We also find an extremely lowtension of the interface between the modulated phase and the vapor/liquidphases. 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 detectsuch low tensions, a new simulation method is proposed. We also consider thecase of d=2 dimensions. The modulated phase then does not survive, leading to aradically different phase diagram.

Phase separation in fluids exposed to spatially periodic external fields