Topological Susceptibility of the 2d O(3) Model under Gradient Flow
| Autor: | Bietenholz, Wolfgang, de Forcrand, Philippe, Gerber, Urs, Mejía-Díaz, Héctor, Sandoval, Ilya O. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Phys. Rev. D 98, 114501 (2018) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.98.114501 |
| Popis: | 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 $\chi_{\rm t}$ does not scale towards a finite continuum limit. Previous numerical studies confirmed that the quantity $\chi_{\rm t}\, \xi^{2}$ 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 $\chi_{\rm t}$. 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. Comment: 26 pages, 9 figures, 2 tables, final version to appear in Phys. Rev. D |
| Databáze: | arXiv |
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