Determination of growth exponent for percolating clusters of various lattices

Abstract

A computer simulation experiment has been carried out near the critical region of percolation clusters of various lattices. This certain growth exponent/spreading velocity exponent has been determined by put on the scaling theory on this percolating cluster near the critical region (i.e., P = Pc ). This exponent is named in a different way in not the same context. Owing to this enormous usage of this exponent to the real physical system, we focus our attention to find this exponent. The value of this exponent is determined for the normal conducting lattices like square, triangular & honey comb and superconducting Ortho I phase & Ortho II phase for different lattice dimensions. From the experiment it is detected that, if the concentration of the site occupancy increases, the spreading velocity or the value of growth exponent is also increases naturally. All the values are found to be less than one, indicating large spreading nature or growth nature physically as per the scaling laws. From our experiments it is found to be the exponent values fall between 0.2 and 0.5 for all lattice dimensions irrespective of lattice type.