Nonequilibrium phase transition in a model of diffusion, aggregation, and fragmentation

We study the nonequilibrium phase transition in a model of aggregation of m asses allowing for diffusion, aggregation on contact, and fragmentation. Th e model undergoes a dynamical phase transition in all dimensions. The stead y-state mass distribution decays exponentially for large mass in one phase. In the other phase, the mass distribution decays as a power law accompanie d, in addition, by the formation of an infinite aggregate. The model is sol ved exactly within a mean-field approximation which keeps track of the dist ribution of masses. In one dimension, by mapping to an equivalent lattice g as model, exact steady states are obtained in two extreme limits of the par ameter space. Critical exponents and the phase diagram are obtained numeric ally in one dimension. We also study the time-dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exp onent chi and the dynamical exponent z analytically in some limits and nume rically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statisti cal mechanics.