content_image/333708.jpg
<img src='content_image/333708.jpg'>

Here x$_{rms}$ represents the longitudinal cluster size (i.e., its length), while y$_{rms}$ is the trans- verse cluster width. In particular, y$_{rms}$ can be used as an order parameter for the zigzag transition since y$_{rms}$ = 0 in the 1D straight line configuration and y$_{rms}$ > 0 for the 2D zigzag configuration [16]. 

The measured c.m. frequencies ω$_{x}$ and ω$_{y}$ are plotted vs d in Fig. 3(a). Here ω$_{x}$ (the frequency associated with the fixed 50.8 mm separation) shows a weak linear increase with 

