Shattering transition in a multivariable fragmentation model

We introduce a linear fragmentation model in which the fragments are described by two correlated variables x and y, and for the power law breakup rate a(x,y)=xαyβ, we derive its exact solution. The large fluctuations of the additional variable prevent any mean-field reduction to a one-variable model. New features, such as shattering with power law decay of the mass, are obtained