Percolation of finite-sized objects on a lattice

We study the percolation of finite-sized objects on two- and three-dimensional lattices. Our motivation stems, on one hand, from some recent interesting experimental results on transport properties of impurity-doped oxide perovskites, and on the other hand from the theoretical appeal that this problem presents. Our system exhibits a well-defined percolation threshold. We estimate the size of magnetic polarons, believed to be the carriers of the above-mentioned transport. We have also obtained two critical exponents for our model, which characterize its universality class.