Charge distribution in two-dimensional electrostatics

I. Kogan, A. M. Perelomov, G. W. Semenoff

We examine the stability of ringlike configurations of N charges on a plane interacting through the potential $V(z_1,...,z_N)={\sum }_i|z_i{|}^2-{\sum }_{i<j}ln|z_i-z_j{|}^2$. We interpret…