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The grand canonical partition functions for primitive droplet nucleationmodels with an excess energy epsilon_n = - mu n + sigma n^{1-eta}, eta = 1/d,for droplets of n constituents in d dimensions are calculated exacly in closedform in the cases d=2 and 3 for all (complex) mu by exploiting the fact thatthe partition functions obey simple PDE.Comment: 10 pages, Latex; References and a cross-check of the main result -  unchanged - added, misprints correcte

Exact Partition Functions for the Primitive Droplet Nucleation Model in Two and Three Dimensions