We introduce and analyse a class of fragmentation-coalescence processes
defined on finite systems of particles organised into clusters. Coalescent
events merge multiple clusters simultaneously to form a single larger cluster,
while fragmentation breaks up a cluster into a collection of singletons. Under
mild conditions on the coalescence rates, we show that the distribution of
cluster sizes becomes non- random in the thermodynamic limit. Moreover, we
discover that in the limit of small fragmentation rate these processes exhibit
self-organised criticality in the cluster size distribution, with universal
exponent 3/2.Comment: 17 pages, 1 figur
