Asymptotic scaling of the mass gap in the two-dimensional O(3) nonlinear σ model: A numerical study

For the two-dimensional standard O(3) nonlinear σ model with the Hamiltonian H=-β ${\mathcal{J}}_{\mathrm{〈}\mathit{i}\mathit{j}\mathrm{〉}}$ ${\mathrm{\sigma }}_{\mathit{i}}$⋅${\mathrm{\sigma }}_{\mathit{j}}$, we report a bulk correlation length (${\xi }_{\mathrm{\infty }}$) up to β=2.7 (where the corresponding ${\xi }_{\mathrm{\infty }}$≃15 000) obtained based on a finite-size-scaling Monte Carlo technique. We find that asymptotic scaling starts to set in around β=2.3, and that the analytical prediction on ${\xi }_{\mathrm{\infty }}$ by Hasenfratz, Maggiore, and Niedermayer agrees better with data as β increases.