Determine the nature of the finite-temperature transition

Determine whether the apparent finite-temperature transition of the frustrated J1-J2 Ising model on the honeycomb lattice is a crossover without thermodynamic singularities, a continuous finite-order phase transition, or a Berezinskii-Kosterlitz-Thouless transition for J2 = −0.5 and J2 = −1.

Background

For J2 = −0.5 and J2 = −1, the simulations show transition-like behavior in the specific heat and nematic observables. However, strong finite-size corrections, sensitivity to boundary conditions and aspect ratio, and slow frustrated dynamics prevent the authors from identifying the thermodynamic behavior. The unresolved alternatives are a nonsingular crossover, a conventional continuous transition, or a BKT transition.

References

For the potential transition at temperatures β ≈ 2.46 (J2 = −0.5) and β ≈ 1.2 (J2 = −1), we find that there are three possible scenarios: i) a crossover without any singularities, ii) a continuous phase transition, or iii) a BKT transition. Unfortunately, given the strong scaling corrections, the sensitive dependence on boundary conditions and aspect ratios, and the slow dynamics connected to the inherent frustration, our data do not allow us to reach a final decision for one of the above scenarios.

— Meandering stripes in the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice  (2608.21261 - Gessert et al., 21 Aug 2026) in Section V, Discussion