  Our measurements of the differential susceptibility dM/dH of the frustrated
magnetic molecules Mo72Fe30 and Mo72Cr30 reveal a pronounced dependence on
magnetic field (H) and temperature (T) in the low H - low T regime, contrary to
the predictions of existing models. Excellent agreement with experiment is
achieved upon formulating a nearest-neighbor classical Heisenberg model where
the 60 nearest-neighbor exchange interactions in each molecule, rather than
being identical as has been assumed heretofore, are described by a
two-parameter probability distribution of values of the exchange constant. We
suggest that the probability distribution provides a convenient
phenomenological platform for summarizing the combined effects of multiple
microscopic mechanisms that disrupt the idealized picture of a Heisenberg model
based on a single value of the nearest-neighbor exchange constant.
