UNIVERSAL CRITICAL EXPONENTS AND SCALING FUNCTIONS IN CONTINUUM PERCOLATION

Many interesting problems in solid state and condensed matter physics are represented more appropriately by continuum percolation model (CPM ) rather than lattice percolation model (LPM). However, our understand ing of CPM is far less than LPM due to difficulty in the analytic and numerical studies of CPM. In this paper we use a random deposition pro cess and a multiple-labeling technique to study continuum percolation of soft disks and hard disks in two dimensions. We find strong evidenc es that critical exponents of soft disks and hard disks are in the sam e universality class as percolation models on planar lattices. Our res ults also indicate that soft disks, hard disks, and planar lattice per colation models have universal finite-size scaling functions. Similar results are found for continuum percolation in three dimensional space .