We analyze the fragmentation behavior of random clusters on the lattice under a process
where bonds between neighboring sites are successively broken. Modeling such structures
by configurations of a generalized Potts or random-cluster model allows us to discuss a wide
range of systems with fractal properties including trees as well as dense clusters. We
present exact results for the densities of fragmenting edges and the distribution of fragment
sizes for critical clusters in two dimensions. Dynamical fragmentation with a size cutoff leads …

Breakup phenomena are ubiquitous in nature and technology. They span a vast range of
time and length scales, including polymer degradation as well as collision induced
fragmentation of asteroids. In geology, fragmentation results in the distribution of grain sizes
observed in soils; fluids break up into droplets and fluid structures such as eddies undergo
fragmentation. On the subatomic scale, excited atomic nuclei break up into fragments.
Practical applications, such as mineral processing, ask for optimizations according to …