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We investigate the partition function zeros of the two-dimensional $p$-stateclock model in the complex temperature plane by using the Wang-Landau method.For $p=5$, $6$, $8$, and $10$, we propose a modified energy representation toenumerate exact irregular energy levels for the density of states without anybinning artifacts. Comparing the leading zeros between different $p$'s, weprovide strong evidence that the upper transition at $p=6$ is indeed of theBerezinskii-Kosterlitz-Thouless (BKT) type in contrast to the claim of theprevious Fisher zero study [Phys. Rev. E \textbf{80}, 042103 (2009)]. We findthat the leading zeros of $p=6$ at the upper transition collapse onto the zerotrajectories of the larger $p$'s including the $XY$ limit while the finite-sizebehavior of $p=5$ differs from the converged behavior of $p \ge 6$ within thesystem sizes examined. In addition, we argue that the nondivergent specificheat in the BKT transition is responsible for the small partition functionmagnitude that decreases exponentially with increasing system size near theleading zero, fundamentally limiting access to large systems in search forzeros with an estimator under finite statistical fluctuations.

Partition function zeros of the p-state clock model in the complex temperature plane