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We investigate systematically the local field distribution functions of up-spins for systems of dipolar interaction,with particular emphasis on Ising-type lattice systems.It is found that as the fraction increases,the shape of the distribution function changes from Lorentzian to Gaussian.In addition,sub-peaks can be induced in the distribution function by non-cubic lattice structures.This is in stark contrast with a dilute gas system,where the distribution has only one Lorentzian peak for any up-spin fraction.