Physical models on random lattices
The thesis will consist of five main chapters. In Chapter 1 a general description of random lattices and their geometrical properties will be given as well as a discussion of the formulation of random lattice field theory. The details of the construction of random lattices will be given in an appendix. In Chapter 2 there will be a discussion of the results of a simulation of the XY-model on a two dimensional random lattice. This simulation was carried out with the intention of comparing the behaviour of the XY-model on regular and random lattices. Chapter 3 will contain the results of a simulation of percolation models on random lattices using the technique of invasion percolation. In Chapter 4 there will be a proof that the problem of continuum percolation of disks can be formulated as a particular correlated bond percolation problem on a two dimensional random lattice. A simulation of continuum percolation based on the result of this proof will be described. The final chapter, Chapter 5, will be about diffusion in invasion percolation clusters.