# The particle mesh ewald method in two dimensions

I am attempting to implement the particle mesh ewald method (http://dx.doi.org/10.1063/1.470117) in two dimensions. I am wondering what needs to be changed in the method from three dimensions to two dimensions? One thing I have recently discovered is that the electrostatic potential in two dimensions has a different formula (something like $-q_iq_j\text{log}(r_{ij})$) rather than $\frac{q_1q_2}{r_{ij}}$ as is stated in the paper. If anyone could shed some light on the particle mesh ewald method in two dimensions, and my issue with the electrostatic potential formula, that would be helpful. Cheers

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A free pdf file is currently available from the second author's homepage (scroll down to ref. 44). –  Qmechanic Oct 15 '12 at 15:17