  We study avalanches in a model for a planar crack propagating in a disordered
medium. Due to long-range interactions, avalanches are formed by a set of
spatially disconnected local clusters, the sizes of which are distributed
according to a power law with an exponent $\tau_{a}=1.5$. We derive a scaling
relation $\tau_a=2\tau-1$ between the local cluster exponent $\tau_a$ and the
global avalanche exponent $\tau$. For length scales longer than a cross-over
length proportional to the Larkin length, the aspect ratio of the local
clusters scales with the roughness exponent of the line model. Our analysis
provides an explanation for experimental results on planar crack avalanches in
Plexiglas plates, but the results are applicable also to other systems with
long-range interactions.
