A two-dimensional model of pair aggregation

We modify the usual percolation theory (PT) by subtituting single particles which occupy sites on a two-dimensional square lattice, by pairs of particles linked by strings whose maximum length is a multiple of the basic lattice spacing. The crossing of random length strings of the pairs leads to entanglements and clusters are formed. We analyze the critical behaviour of this model as a function of the pair occupation fraction, p. Within the accuracy provided by the Monte Carlo simulations all the critical exponents obtained are compatible with their standard PT counterparts. Thus, the ordinary scaling relations are fulfilled.