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

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 regularized version, but semiclassical arguments suggest that the topological susceptibility χt does not scale towards a finite continuum limit. Previous numerical studies confirmed that the quantity χtξ2 diverges at large correlation length ξ. 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 χt. However, even when the flow time is so long that the GF impact range—or smoothing radius—attains ξ/2, we still do not observe evidence of continuum scaling.