Abstract
We study monolayer formation on a polycrystalline substrate with quenched, random impurities using the equivalence to the two-dimensional random-field Ising model. From renormalization-group (RG) arguments, we obtain expressions for the zero-field susceptibility ${\ensuremath{\chi}}_{0}$ as a function of the linear dimension of a typical crystallite and the width of the field distribution. This work generalizes recent results on finite-size effects at first-order phase transitions. The Curie-law divergence of ${\ensuremath{\chi}}_{0}$ at low temperatures found for pure finite-sized crystallites is removed in the presence of impurities. The validity of our results is supported by a Migdal-Kadanoff RG calculation.
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