It seems that there is a problem of interpretation in this articel. There is no long range order parameter the BKT phase transition because of the Mermin-Wagner theorem at least in the 2DXY model. The magnetisation M is 0 at all temperatures for the 2DXY model. The magnetisation found in this article $M =exp(-c/(\sqrt{T_c-T})$ could be related to a 3DXY or something like that.
I don't understand the BKT interpretation in this article.
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