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. 2021 Aug 5;11:15937. doi: 10.1038/s41598-021-95595-2

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© The Author(s) 2021

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Characteristic length $r_{0}$ of the ferromagnetic 2D Ising model. The zero crossings of the computed CCF are plotted in linear–linear (left), log–linear (middle) and log–log (right) axis. Top three panels correspond to different system sizes L and bottom three panels to different window lengths W. Different symbols correspond to the values of the temperature T denoted in the legends. Dashed lines are visual aids to emphasize the predicted logarithmic behavior for both sub-critical and super-critical regimes (open circles), and the linear dependence expected for the critical regime (filled circles). Open triangles are used to denote results obtained for intermediate values of temperature indicated in the legend. In all cases, error bars are omitted, since error estimates are smaller than symbol size.