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 $\mathfrak{Re}(T)\le T_{BKT}$ 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.

References in corpus (3)

• Scalable replica-exchange framework for Wang-Landau sampling
• Phase transitions in the complex plane of physical parameters
• Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: A comparison for elastic flexible polymers

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