A model of pair aggregation

Inspired by the familiar phenomenon of the cherry entanglement, we compute the clustering properties of a new model in which pairs of elements, located on the sites of a lattice and tiling it completely, attach to form aggregates of various sizes. Avoiding double-occupancy, the distance between the two elements of each pair is chosen at random with a prescribed maximum lenght, l. The resulting clustering behaviour crucially depends on the dimension of the embedding lattice and on l. We devise a transfer-matrix method to solve the model in 1 dimension. Results in 2 dimensions are obtained by Monte Carlo simulations. In 1 dimension, we define a characteristic cluster size: it depends exponentially on l. In 2 dimensions, for a big enough l, we find scaling for the probability of occurrence of clusters of size n versus n. Possible generalizations of this model are qualitatively discussed.