content_image/410752.jpg content_image/410757.jpg content_image/410753.jpg
<img src='content_image/410752.jpg'>

<img src='content_image/410757.jpg'>

<img src='content_image/410753.jpg'>

over a wide distance. For δ$_{0}$ > 6 $^{◦}$, on the other hand, the correlation is short-ranged and decays more slowly than exponential. The qualitative change in the correlation function gives another support of the above estimate of the threshold angle, δ$_{th}$ = 6 $^{◦}$. 

Mean-field theory. - Now we apply a mean-field ap- proximation to our model. When the coupling is weak ( γ ≪ 1) and the force angle is small ( δ$_{0}$ ≪ 1), we can neglect the δ$_{j}$ ’s in the RHS of eq. (2) because they give 

