Vortex triangular lattice

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  • Thread starter Einj
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Hello everyone,
I am not an expert in the topic so I apologize in advance if the question has an easy answer. I think it is well known that if we have a set of N vortices in a superfluid their mutual interaction is logarithmic. Meaning that if [itex]\vec x_n[/itex] is the position of the n-th vortex, then the potential between them is of the form

$$
V(\{\vec x_n\})\propto-\sum_{n=1}^N\sum_{m<n}\log|\vec x_n-\vec x_m|
$$

I also know that the vortices will arrange themselves on a triangular lattice.

Does anyone know how to show that starting from the previous potential?

Thanks!
 

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