| 1485 |
|
the effective moment, $\bar{Q}^2 = \frac{2}{3} \Theta : \Theta$.) |
| 1486 |
|
|
| 1487 |
|
\begin{figure} |
| 1488 |
< |
\includegraphics[width=\linewidth]{Quadrupoles_rcutConvergence-crop.pdf} |
| 1489 |
< |
\caption{Convergence to the analytic energy constants as a function of |
| 1490 |
< |
cutoff radius (normalized by the lattice constant) for the different |
| 1491 |
< |
real-space methods for (a) dipolar and (b) quadrupolar crystals.The energy constants for hard, SP, GSF, TSF and analytic methods are represented by black sold-circle, red solid-square,green solid-diamond and grey dashed line respectively. |
| 1492 |
< |
The left panel shows results for the undamped kernel ($1/r$), while the damped |
| 1493 |
< |
error function kernel, $B_0(r)$ was used in the right panel. } |
| 1494 |
< |
\label{fig:QuadrupolesrcutCovergence-crop.pdf} |
| 1488 |
> |
\includegraphics[width=\linewidth]{Quadrupoles_rcutConvergence.pdf} |
| 1489 |
> |
\caption{Convergence of the lattice energy constants as a function of |
| 1490 |
> |
cutoff radius (normalized by the lattice constant, $a$) for the new |
| 1491 |
> |
real-space methods. Three quadrupolar crystal structures were |
| 1492 |
> |
sampled, and the analytic energy constants for the three lattices |
| 1493 |
> |
are indicated with grey dashed lines. The left panel shows results |
| 1494 |
> |
for the undamped kernel ($1/r$), while the damped error function |
| 1495 |
> |
kernel, $B_0(r)$ was used in the right panel.} |
| 1496 |
> |
\label{fig:QuadrupolesrcutCovergence} |
| 1497 |
|
\end{figure} |
| 1498 |
|
|
| 1499 |
|
|
