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

TL;DR

This paper investigates the O(n) non-linear sigma-model on 2D regular and random lattices, analyzing mass gaps and topological susceptibility to understand the effects of lattice randomness on the model's properties.

Contribution

It provides a detailed simulation of the sigma-model on random lattices, comparing results with regular lattices and previous semi-analytical calculations.

Findings

Ratios of Lambda parameters agree with semi-analytical predictions

Mass gap analysis shows consistent asymptotic scaling

Topological susceptibility computed via cooling method

Abstract

The O(n) non-linear $\sigma$-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 $\Lambda_{\rm random}/\Lambda_{\rm regular}$. These ratios are in agreement with previous semi-analytical calculations. We also numerically calculate the topological susceptibility by using the cooling method.