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# Signatures of the Berezinskii-Kosterlitz-Thouless transition on the location of the zeros of the canonical partition function for the 2D XY-model

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### Abstract

In this work we show how one can use the zeros of the canonical partition function, the Fisher zeros, to unambiguously characterize a transition as being in the Berezinskii-Kosterlitz-Thouless ($$BKT$$) class of universality. By studying the zeros map for the 2D XY-model, we found that its internal border coalesces into the real positive axis in a finite region corresponding to temperatures smaller than the $$BKT$$ transition temperature. This behavior is consistent with the predicted existence of a line of critical points below the transition temperature, allowing one to distinguish the $$BKT$$ class of universality from other possibilities.

### Author and article information

###### Journal
2015-07-08
2015-07-25
###### Article
10.1016/j.cpc.2016.08.016
1507.02231
85facc12-dae0-439f-905e-6ff02e38991a