Ising model on 2D random lattices

Abstract

We report single-cluster Monte Carlo simulations of the Ising model on two-dimensional Poissonian random lattices constructed according to the Voronoi/Delaunay prescription. One set of simulations is performed near criticality on lattices with up to 80 000 sites. Here we apply reweighting techniques to obtain the critical exponents from a finite-size scaling analysis. The other set of simulations is performed in the disordered phase and the critical parameters are extracted from fits to power-law divergencies as the critical point is approached. From both sets we obtain unambiguous support for lattice universality, i.e., that the critical exponents of the Ising model on a two-dimensional random lattice agree with the exactly known values for regular lattices.