  We investigate the size scaling of the macroscopic fracture strength of
heterogeneous materials when microscopic disorder is controlled by fat-tailed
distributions. We consider a fiber bundle model where the strength of single
fibers is described by a power law distribution over a finite range. Tuning the
amount of disorder by varying the power law exponent and the upper cutoff of
fibers' strength, in the limit of equal load sharing an astonishing size effect
is revealed: For small system sizes the bundle strength increases with the
number of fibers and the usual decreasing size effect of heterogeneous
materials is only restored beyond a characteristic size. We show analytically
that the extreme order statistics of fibers' strength is responsible for this
peculiar behavior. Analyzing the results of computer simulations we deduce a
scaling form which describes the dependence of the macroscopic strength of
fiber bundles on the parameters of microscopic disorder over the entire range
of system sizes.
