Real space electrostatics for multipoles. III. Dielectric properties

Unsolved problem of long-range interactions: dipolar spin-ice study

Long-range interactions derive various strange phenomena. As illustrated by cutoff simulations of water, increasing cutoff length does not improve the simulation result necessarily; on the contrary, it makes the result worse. In the extreme situation, the structure of water transforms into a layer structure. In this study, to explore the underlying mechanism of this phenomenon, we performed Monte Carlo simulations on dipolar spins arranged on a pyrochlore spin-ice lattice. Like the water case, the present dipolar spin system also showed cutoff-induced dipole ordering and layer formation. The width of the layers depended on the cutoff length; and longer cutoff length led to a broader layer. These features are certainly consistent with the previous water case. This indicates that layer formation is the general behavior of dipolar systems whose interactions are truncated within a finite distance. The result is important for future exploration of the relationship between long-range interactions and resulting structures. In addition, it emphasizes the necessity of rigorous treatment of long-range interactions because increasing the cutoff length prevents convergence and provides an entirely different result from the rigorous Ewald calculation.

Dielectric continuum model examination of real-space electrostatic treatments

Electrostatic interaction is long ranged; thus, the accurate calculation is not an easy task in molecular dynamics or Monte Carlo simulations. Though the rigorous Ewald method based on the reciprocal space has been established, real-space treatments have recently become an attractive alternative because of the efficient calculation. However, the construction is not yet completed and is now a challenging subject. In an earlier theoretical study, Neumann and Steinhauser employed the Onsager dielectric continuum model to explain how simple real-space cutoff produces artificial dipolar orientation. In the present study, we employ this continuum model to explore the fundamental properties of the recently developed real-space treatments of three shifting schemes. The result of the distance-dependent Kirkwood function G_K(R) showed that the simple bare cutoff produces a well-known hole-shaped artifact, whereas the shift treatments do not. Two-dimensional mapping of electric field well explained how these shift treatments remove the hole-shaped artifact. Still, the shift treatments are not sufficient because they do not produce a flat G_K(R) profile unlike ideal no-cutoff treatment. To test the continuum model results, we also performed Monte Carlo simulations of dipolar particles. The results found that the continuum model could predict the qualitative tendency as to whether each electrostatic treatment produces the hole-shaped artifact of G_K(R) or not. We expect that the present study using the continuum model offers a stringent criterion to judge whether the primitive electrostatic behavior is correctly described or not, which will be useful for future construction of electrostatic treatments.