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

TL;DR

This paper investigates pattern formation in a 2D dipolar Ising model on a honeycomb lattice using Monte Carlo simulations, revealing similar behaviors to square lattices but with sixfold symmetry, and introduces a new method for handling long-range interactions.

Contribution

It provides new insights into dipolar Ising models on honeycomb lattices and proposes a simplified method for evaluating long-range dipolar interactions.

Findings

Structures reflect sixfold symmetry of honeycomb lattice.

Thermodynamic properties are similar to square lattice case.

Introduces a straightforward method for effective interaction calculation.

Abstract

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.