Topological Susceptibility of the 2d O(3) Model under Gradient Flow

Abstract

The 2d O(3) model is widely used as a toy model for ferromagnetism and for Quantum Chromodynamics. With the latter it shares --- among other basic aspects --- the property that the continuum functional integral splits into topological sectors. Topology can also be defined in its lattice regularised version, but semi-classical arguments suggest that the topological susceptibility ${\chi }_{\mathrm{t}}$ does not scale towards a finite continuum limit. Previous numerical studies confirmed that the quantity ${\chi }_{\mathrm{t}}{\xi }^2$ diverges at large correlation length $\xi$. Here we investigate the question whether or not this divergence persists when the configurations are smoothened by the Gradient Flow (GF). The GF destroys part of the topological windings; on fine lattices this strongly reduces ${\chi }_{\mathrm{t}}$. However, even when the flow time is so long that the GF impact range --- or smoothing radius --- attains $\xi /2$, we do still not observe evidence of continuum scaling.

26 pages, 9 figures, 2 tables, final version to appear in Phys. Rev. D

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Cited by in corpus (5)

• Is $N=2$ Large?
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• $\theta$-dependence in the small-$N$ limit of $2d$ $C{P}^{N-1}$ models
• Supersymmetric gradient flow in the Wess-Zumino model
• Topology of the O(3) non-linear sigma model under the gradient flow