The magnitude of the exchange bias field of patterned systems exhibits a notable increase in relation to the usual bilayer systems, where a continuous ferromagnetic film is deposited on an antiferromagnet insulator. Here we develop a model, and implement a Monte Carlo calculation, to interpret the experimental observations which is consistent with experimental results, on the basis of assuming a small fraction of spins pinned ferromagnetically in the antiferromagnetic interface layer. (C) 2010 Elsevier B.V. All rights reserved.