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We use the single-cluster Monte Carlo update algorithm to simulate the Isingmodel on two-dimensional Poissonian random lattices with up to 80,000 siteswhich are linked together according to the Voronoi/Delaunay prescription. Inone set of simulations we use reweighting techniques and finite-size scalinganalysis to investigate the critical properties of the model in the veryvicinity of the phase transition. In the other set of simulations we study theapproach to criticality in the disordered phase, making use of improvedestimators for measurements. From both sets of simulations we obtain clearevidence that the critical exponents agree with the exactly known exponents forregular lattices, i.e., that (lattice) universality holds for thetwo-dimensional Ising model.Comment: uuencoded postscript file, 34 pages, preprint UAB-FT-32

Single-cluster Monte Carlo study of the Ising model on two-dimensional random lattices