The interesting effects resulting from a linearly varying magnetic field on a thin Ising film is studied. The phase diagram is determined by looking for bulk two-phase coexistence at different values of g, the magnetic field gradient, and temperature T. We confirm the qualitative phase diagram predicted by theoretical work by Rogiers and Indekeu in 1993. As g increases, the temperature bounding bulk two-phase coexistence is re-entrant. We alsostudied non-local correlation functions in Ising films with opposite surface fields by calculating the spin-spin correlations for multiple choices of lattice size L and thickness D, between surface and interface, and within the interface. Fourier transformation of these correlations as well as the ratio between the real-space correlations and their Fourier transformationare calculated. We found that the ratio does decay exponentially as the non-local theory predicted, in the region of small wave vector q. The linear D dependence of the non-local correlation length NL is not confirmed, instead, we observed a power law relationship with the power of 1.20. The values of NL are also estimated.
