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Erratum to: Eur. Phys. J. C (2021) 81:873 https://doi.org/10.1140/epjc/s10052-021-09677-6
In this Erratum we do minor corrections to Table 1, Fig. 4 and Equations (28) and (29). These modifications do not modify any conclusion.
1 First modification
In Table 1, in page 5 of 12, the values of autocorrelation times \(\tau _{P}\) and \(\tau _{Q^{2}}\) for the HMC rows should be doubled. Also, the first sentence of the caption, which reads “Simulation parameters and results for the pure gauge model using \(N_{conf}=5 \cdot 10^5\) configurations in each case” should read “Simulation parameters and results for the pure gauge model using \(N_{\text {conf}}=5 \cdot 10^5\) configurations for wHMC and \(10^6\) for HMC”. The correct table with the corrected caption can be found in this document.
Figure 4, in page 4 of 12, is affected by the modifications of Table 1 and should be changed with a new plot depicting the new data, but its interpretation in text is unchanged. The new figure can be found in this document.
2 Second modification
Equations (28) and (29), in page 5 of 12, are wrong. Their interpretation in the text is unchanged, but a modification of the paragraph prior to Equation (28) is necessary. The suggested modification of the paragraph prior to Equation (28) until Equation (29) follows:
One can understand the improvement of the acceptance rate of the winding step with \(L_{w}\). The change in the action when a winding is performed is restricted to the plaquettes at the boundary of \(S_{w}\), and is due to the change in the links at the boundary—see violet region in Fig. 2. The change in the phase of the plaquette, \(\delta \theta _{p}\), due to the transformation \(\Omega ^{\pm }\) is therefore \(\mp \frac{\pi }{2L_{w}}\). We refer to \(\delta S_{w}\) as the outer boundary of the winding region. For sufficiently large \(L_{w}\), the change in the phase of the plaquette is small and we can approximate
The average of the first term of \(\Delta S\) vanishes, while the last term averages to
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Albandea, D., Hernández, P., Ramos, A. et al. Erratum to: Topological sampling through windings. Eur. Phys. J. C 83, 508 (2023). https://doi.org/10.1140/epjc/s10052-023-11683-9
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DOI: https://doi.org/10.1140/epjc/s10052-023-11683-9