Critical behavior of the 3D Ising model on a poissonian random lattice

The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D ferromagnetic Ising model on 3D Voronoi–Delauney lattices. It is assumed that the coupling factor JJ varies with the distance rr between the first neighbors as J(r)∝e−arJ(r)∝e−ar, with a≥0a≥0. The critical exponents γ/νγ/ν, β/νβ/ν, and νν are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure 3D ferromagnetic Ising model.