The 2-dimensional non-linear sigma-model on a random latice

Abstract

The O(n) non-linear $σ$-model is simulated on 2-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, analysing the asymptotic scaling of the data and computing the ratio of Lambda parameters $Λ_{\rm random}/Λ_{\rm regular}$. These ratios are in agreement with previous semi-analytical calculations. We also numerically calculate the topological susceptibility by using the cooling method.