Two-dimensional nonlinear σ model on a random lattice

The O(n) nonlinear σ model is simulated on two-dimensional regular and random lattices. We use two different levels of randomness in the construction of the random lattices and give a detailed explanation of the geometry of such lattices. In the simulations we calculate the mass gap for n=3, 4, and 8, analyzing the asymptotic scaling of the data and computing the ratio of lambda parameters ${\mathrm{\Lambda }}_{\mathrm{random}}$/${\mathrm{\Lambda }}_{\mathrm{regular}}$. These ratios are in agreement with previous semianalytical calculations. We also numerically calculate the topological susceptibility by using the cooling method.