A MODEL OF PAIR AGGREGATION

Inspired by the familiar phenomenon of the cherry entanglement, we com pute the clustering properties of a new model in which pairs of elemen ts,located on the sites of a lattice and tiling it completely, attach to form aggregates of various sizes. Avoiding double-occupancy, the di stance between the two elements of each pair is chosen at random with a prescribed maximum length, l. The resulting clustering behaviour cru cially depends on the dimension of the embedding lattice and on l. We devise a transfer-matrix method to solve the model in 1 dimension. Res ults in 2 dimensions are obtained by Monte Carlo simulations. In 1 dim ension, we define a characteristic cluster size: it depends exponentia lly on l. In 2 dimensions, for a big enough 1, we find scaling for the probability of occurrence of clusters of size n versus n. Possible ge neralizations of this model are qualitatively discussed.