Methods in Percolation
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Algorithms are presented for the computationally efficient manipulation of graphs. These are subsequently used as the basis of a Monte Carlo method for sampling from the microcanonical ensemble of lattice configurations of a percolation model within a neighbourhood of the critical point.
This new method arbitrarily increments and decrements the number of occupied lattice sites, and is shown to be a generalisation of several earlier, purely incremental, methods. As demonstrations of capability, the method was used to construct a phase diagram for exciton transport on a disordered surface, and to study finite size effects upon the incipient spanning cluster.
Application of the method to the classical site percolation model on the two-dimensional square lattice resulted in an exceptionally precise estimate of the critical threshold. Although this estimate is not in agreement with earlier results, its accuracy was established through an application specific test of randomness, which is also introduced here. The same test suggests that many earlier results have been systematically biased due to the use of deficient pseudorandom number generators. The estimate made here has since been independently confirmed.