Pattern formation in the dipolar Ising model on a two-dimensional honeycomb lattice

We present Monte Carlo simulation results for a two-dimensional Ising model with ferromagnetic nearest-neighbor couplings and a competing long-range dipolar interaction on a honeycomb lattice. Both structural and thermodynamic properties are very similar to the case of a square lattice, with the exception that structures reflect the sixfold rotational symmetry of the underlying honeycomb lattice. To deal with the long-range nature of the dipolar interaction we also present a simple method of evaluating effective interaction coefficients, which can be regarded as a more straightforward alternative to the prevalent Ewald summation techniques.

💡 Research Summary

The paper investigates a two‑dimensional Ising model defined on a honeycomb lattice in which each spin experiences a ferromagnetic nearest‑neighbor exchange (strength J > 0) and a competing long‑range dipolar interaction that decays as 1/r³ (strength D). While similar models on square lattices have been extensively studied, the honeycomb geometry introduces a six‑fold rotational symmetry that can profoundly affect the emergent patterns.

Monte‑Carlo simulations using the Metropolis algorithm were performed for system sizes up to 96 × 96 spins (N ≈ 2L²) and for a range of temperatures T/J ∈