Iron grown on room‐temperature CaF2/Si(111) substrates form two‐dimensional arrays of nanometer‐sized superparamagnetic islands. Deposition of Ag on the Fe/CaF2/Si(111) produced a superparamagnetic response where the effective moment was proportional to the number of Fe islands covered by an average‐sized Ag island. The nonmagnetic Ag overlayer mediates a long‐range exchange between neighboring Fe islands within an individual Ag island. Monte Carlo methods are used to examine ordering in two dimensions and to set minimum interisland coupling strengths. ©1995 American Institute of Physics.