A New Algorithm to Study the Critical Behavior of Topological Phase Transitions
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Topological phase transitions such as the Berezinskii-Kosterlitz-Thouless (BKT) transition are difficult to characterize due to the difficulty in defining an appropriate order parameter or to unravel its critical properties. In this paper, we discuss the application of a newly introduced numerical algorithm that was inspired by the Fisher zeros of the partition function and is based on the partial knowledge of the zeros of the energy probability distribution (EPD zeros). This iterative method has proven to be quite general, furnishing the transition temperature with great precision and a relatively low computational effort. Since it does not need the a priori knowledge of any order parameter it provides an unbiased estimative of the transition temperature being convenient to the study of this kind of phase transition. Therefore, we applied the EPD zeros approach to the 2D XY model, which is well known for showing a BKT transition, in order to demonstrate its effectivity in the study of the BKT transition. Our results are consistent with the real and imaginary parts of the pseudo-transition temperature, T(L), having a different asymptotic behavior, which suggests a way to characterize a BKT like transition.
KeywordsPartition function zeros Topological phase transition XY model Monte Carlo simulations Replica-exchange Wang-Landau
The authors thank CNPq (Grants 303480/2017-3, 306457/2016-4) and FAPEMIG (APQ-03183-16) for the partial financial support.
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