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arXiv · 1808.08129

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

Wolfgang Bietenholz·Philippe de Forcrand·Urs Gerber·Héctor Mejía-Díaz·Ilya O. Sandoval
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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 $χ_{\rm t}$ does not scale towards a finite continuum limit. Previous numerical studies confirmed that the quantity $χ_{\rm t}\, ξ^{2}$ 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 $χ_{\rm t}$. However, even when the flow time is so long that the GF impact range --- or smoothing radius --- attains $ξ/2$, we do still not observe evidence of continuum scaling.

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Wolfgang Bietenholz, Philippe de Forcrand, Urs Gerber, Héctor Mejía-Díaz, Ilya O. Sandoval. 2018-12-05. Topological Susceptibility of the 2d O(3) Model under Gradient Flow. https://doi.org/10.1103/physrevd.98.114501

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