This paper investigates the spectrum of axions radiated from global cosmic string networks in the early universe, focusing on their potential as cold dark matter (CDM). The authors perform extensive numerical simulations of these networks using a large-scale lattice grid, aiming to improve the understanding of the dependence of the axion emission spectrum on the string tension parameter. They find several systematic effects that were previously overlooked, such as the dependence on initial conditions, oscillations in the spectrum, and discretization effects. The study confirms that the spectral index of the axion emission spectrum increases with the string tension but does not provide clear evidence of whether this trend continues or saturates at higher string tensions due to discretization effects. By extrapolating the results with a power-law assumption, the authors predict the dark matter mass to be in the range of \(95-450 \, \mu \text{eV}\). The paper also discusses the attractor behavior of the string network and the impact of oscillations and discretization errors on the estimation of the axion production rate and spectral index.This paper investigates the spectrum of axions radiated from global cosmic string networks in the early universe, focusing on their potential as cold dark matter (CDM). The authors perform extensive numerical simulations of these networks using a large-scale lattice grid, aiming to improve the understanding of the dependence of the axion emission spectrum on the string tension parameter. They find several systematic effects that were previously overlooked, such as the dependence on initial conditions, oscillations in the spectrum, and discretization effects. The study confirms that the spectral index of the axion emission spectrum increases with the string tension but does not provide clear evidence of whether this trend continues or saturates at higher string tensions due to discretization effects. By extrapolating the results with a power-law assumption, the authors predict the dark matter mass to be in the range of \(95-450 \, \mu \text{eV}\). The paper also discusses the attractor behavior of the string network and the impact of oscillations and discretization errors on the estimation of the axion production rate and spectral index.