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

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.