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Intergranular interactions in nanostructured FePt:Ag thin films and their effect on magnetic hysteresis are investigated. The films, produced by multilayer deposition plus rapid thermal annealing, consist of FePt nanoparticles embedded in a silver matrix. They are investigated by magnetization measurements and magnetic force microscopy. Analytical model calculations, supported by micromagnetic simulations, are used to elucidate the relation between coercivity, hysteresis-loop slope, and spatial correlations during magnetization reversal. The analytical calculations yield simple expressions for the loop slope and the coercivity as a function of the intergranular exchange. Small intergranular exchange enhances the coercivity, but for strong exchange there is a self-energy cutoff, associated with the onset of cooperative reversal and preventing alpha from becoming negative.