2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217037The grand canonical partition functions for primitive droplet nucleation models 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 closed form in the cases d=2 and 3 for all (complex) mu by exploiting the fact that the partition functions obey simple PDE.10 pages, Latex; References and a cross-check of the main result - unchanged - added, misprints correctedStatistical MechanicsMathematical Physicstext