Partition function zeros of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice

TL;DR

This paper investigates the zeros of the partition function in a frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice, demonstrating the usefulness of zero analysis in understanding phase transitions and universality classes.

Contribution

It introduces a comparative analysis of Fisher and Lee-Yang zeros with traditional FSS methods, highlighting the effectiveness of zero analysis in complex frustrated systems.

Findings

Partition function zeros indicate the system remains in the Ising universality class for $ ext{J}_2/ ext{J}_1$ down to -0.22.

Zero analysis provides clearer insights into phase boundaries amid strong corrections to scaling.

Cumulant method convergence depends on cumulant order, guiding practical implementation.

Abstract

We study the zeros of the partition function in the complex temperature plane (Fisher zeros) and in the complex external field plane (Lee-Yang zeros) of a frustrated Ising model with competing nearest-neighbor ($J_1 > 0$) and next-nearest-neighbor ($J_2 < 0$) interactions on the honeycomb lattice. We consider the finite-size scaling (FSS) of the leading Fisher and Lee-Yang zeros as determined from a cumulant method and compare it to a traditional scaling analysis based on the logarithmic derivative of the magnetization $\partial \ln \langle |M| \rangle /\partial\beta$ and the magnetic susceptibility $\chi$. While for this model both FSS approaches are subject to strong corrections to scaling induced by the frustration, their behavior is rather different, in particular as the ratio $\mathcal{R} = J_2/J_1$ is varied. As a consequence, an analysis of the scaling of partition function zeros turns out to be a useful complement to a more traditional FSS analysis. For the cumulant method, we also study the convergence as a function of cumulant order, providing suggestions for practical implementations. The scaling of the zeros convincingly shows that the system remains in the Ising universality class for $\mathcal{R}$ as low as $-0.22$, where results from traditional FSS using the same simulation data are less conclusive. The approach hence provides a valuable additional tool for mapping out the phase diagram of models afflicted by strong corrections to scaling.