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Wetting transitions are studied in the two-dimensional Ising ferromagnet confined between walls wherecompetitive surface fields act. In our finite samples of size L ×M, the walls are separated by a distance L, Mbeing the length of the sample. The surface fields are taken to be short-range and nonuniform, i.e., of the formH1,δH1,H1,δH1, . . ., where the parameter −1 δ 1 allows us to control the nonuniformity of the fields. Byperforming Monte Carlo simulations we found that those competitive surface fields lead to the occurrence of aninterface between magnetic domains of different orientation that runs parallel to the walls. In finite samples, suchan interface undergoes a localization-delocalization transition, which is the precursor of a true wetting transitionthat takes place in the thermodynamic limit. By exactly working out the ground state (T = 0), we found thatbesides the standard nonwet and wet phases, a surface antiferromagnetic-like state emerges for δ < −1/3 andlarge fields (H1 > 3), Htr1 /J = 3, δtr = −1/3,T = 0, being a triple point where three phases coexist. By meansof Monte Carlo simulations it is shown that these features of the phase diagram remain at higher temperatures;e.g., we examined in detail the case T = 0.7 × Tcb. Furthermore, we also recorded phase diagrams for fixedvalues of δ, i.e., plots of the critical field at the wetting transition (H1w) versus T showing, on the one hand, thatthe exact results of Abraham [Abraham, Phys. Rev. Lett. 44, 1165 (1980)] for δ = 1 are recovered, and on theother hand, that extrapolations to T → 0 are consistent with our exact results. Based on our numerical resultswe conjectured that the exact result for the phase diagram worked out by Abraham can be extended for the caseof nonuniform fields. In fact, by considering a nonuniform surface field of some period λ, with λ M, e.g.,[H1(x,λ) > 0], one can obtain the effective fieldHeff at a λ coarse-grained level given byHeff = 1λλx=1 H1(x,λ).Then we conjectured that the exact solution for the phase diagram is now given by Heff/J = F(T ), where F(T )is a function of the temperature T that straightforwardly follows from Abraham?s solution. The conjecture wasexhaustively tested by means of computer simulations. Furthermore, it is found that for δ = 1 the nonwet phasebecomes enlarged, at the expense of the wet one, i.e., a phenomenon that we call ?surface nonuniformity-inducednonwetting,? similar to the already known case of ?roughness-induced nonwetting.