Universality and finite-size effect in the partition function zero of a Wang-Landau-sampled density of states

Abstract

The zeros of partition function often provide an alternative yet systematic way to understand phase transitions without directly measuring a relevant order parameter. Here we investigate how numerical errors in an approximate Wang-Landau density of state affect the evaluation of the partition function zero in complex temperature plane. We introduce two simple systems of the two-dimensional Ising model and the six-state clock model to exemplify the success and failure in the application of the Wang-Landau sampling to the finite-size-scaling analysis of the leading zero. By numerically estimating the fluctuations of the resulting partition function, we argue that the behavior of specific heat at phase transition implies the essential finite- size effects that the Wang-Landau approach may encounter in the partition function zero analysis.