Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition

Abstract

Using the two dimensional \(XY-(S(O(3))\) model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless (\(BKT\)) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the \(BKT\) class of universality. We obtain \(T_{BKT}\) in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions \(\mathfrak{Re}(T) \leq T_{BKT}\) and \(\mathfrak{Re}(T) > T_{BKT}\) in the thermodynamic limit show that \(\mathfrak{Im}(T)\) goes to zero in the former case and is finite in the last one.