Thin Ising films with both competing surface fields and a magnetic field gradient: A Monte Carlo study

Extensive Monte Carlo simulations are used to study the interesting effects resulting from a linearly varying magnetic field on a thin Ising film (equivalent to applying gravity to the corresponding lattice-gas model). Besides competing surface fields acting on two LxL free surfaces a distance D apart from each other, we also apply a magnetic field g that varies linearly between the surfaces and which competes with the surface fields. To determine the phase diagram, we look for bulk two-phase conexistence at different values of g and temperature T. In situations with only competing surface fields applied, the interface unbinding transition \footnote{K.Binder, D.P.Landau, A.M.Ferrenberg, Phys.Rev.E {\bf 51}, 2824(1995)} happens at temperature T$_{c}$(D). The addition of the g field produces a phase diagram in which, as g increases, the temperature bounding bulk two-phase coexistence first goes up from T$_{c}$(D), and then decreases. For small g, we find a second order transition, whereas for large g, the transition appears to be first order. We will compare our simulation results with theoretical predictions \footnote{J.Rogiers, J.O.Indekeu, Europhys.Lett. {\bf 24}, 21(1993)}. \\ \\ $^*$Research supported by NSF