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In this paper, we present a particle-cluster model for a two-dimensional fractal aggregation with the nearest neighbor and next-nearest neighbor interactions in external fields. The external field is described by the probability P. Our computer simulation results show that the threshold concentration is P-c(a) = 0.59 +/- 0.02 and the fractal dimension is D-c = 1.67 +/- 0.03 at this concentration. In comparison with previous results with nearest neighbor interaction only, we find that D-c is the same, but P-c(a) is smaller, which is reasonable, since the connectivity has been changed significantly.

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