Sample-to-sample noise of the Wang-Landau sampling in the Fisher zero calculations of the 2D Ising model

Abstract

We investigate the effectiveness of the Wang-Landau (WL) sampling for the density of states (DOS) in the partition-function-zero analysis of phase transitions, by employing the two-dimensional Ising model as an example. We compare the lowest zero computed from the Wang-Landau density of states with the one from the exact density of states. We find that the errors in the WL DOS are systematically kept below the accuracy level needed for the determination of the lowest zero for system sizes up to 256 x 256 lattice sites. The location of the lowest zero from the WL DOS numerically agrees very well with that from the exact density of states, and we argue that the finite size scaling characteristics of the Fisher zero are closely related to the performance of the WL approach.