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 TBKT in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions Re(T)≤TBKT and Re(T)>TBKT in the thermodynamic limit shows that Im(T) goes to zero in the former case and is finite in the last one.