  We use the single-cluster Monte Carlo update algorithm to simulate the Ising
model on two-dimensional Poissonian random lattices with up to 80,000 sites
which are linked together according to the Voronoi/Delaunay prescription. In
one set of simulations we use reweighting techniques and finite-size scaling
analysis to investigate the critical properties of the model in the very
vicinity of the phase transition. In the other set of simulations we study the
approach to criticality in the disordered phase, making use of improved
estimators for measurements. From both sets of simulations we obtain clear
evidence that the critical exponents agree with the exactly known exponents for
regular lattices, i.e., that (lattice) universality holds for the
two-dimensional Ising model.
