| 420 |
|
estimated by measuring peak-to-trough distances in |
| 421 |
|
$h(q_{\mathrm{rip}})$ itself. |
| 422 |
|
|
| 423 |
+ |
\begin{figure}[ht] |
| 424 |
+ |
\centering |
| 425 |
+ |
\caption{Contours of the height-dipole correlation function as a function |
| 426 |
+ |
of the dot product between the dipole ($\hat{\mu}$) and inter-dipole |
| 427 |
+ |
separation vector ($\hat{r}$) and the distance ($r$) between the dipoles. |
| 428 |
+ |
Perfect height correlation (contours approaching 1) are present in the |
| 429 |
+ |
ordered phase when the two dipoles are in the same head-to-tail line. |
| 430 |
+ |
Anti-correlation (contours below 0) is only seen when the inter-dipole |
| 431 |
+ |
vector is perpendicular to the dipoles. } |
| 432 |
+ |
\includegraphics[width=\linewidth]{height-dipole-correlation.pdf} |
| 433 |
+ |
\label{fig:CrossCorrelation} |
| 434 |
+ |
\end{figure} |
| 435 |
+ |
|
| 436 |
|
A second, more accurate, and simpler method for estimating ripple |
| 437 |
|
shape is to extract the wavelength and height information directly |
| 438 |
|
from the largest non-thermal peak in the undulation spectrum. For |
