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.

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