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.