Journal of Statistical Physics, Vol. 34, Nos. 3/4, 1984. p. 557-569.
We supplement a previous paper on three-dimensional systems by studying the electric potential and field fluctuations in two-dimensional Coulomb systems. The novelty in two dimensions is that the fluctuations of the potential at a point are infinite in the thermodynamic limit. However, the potential difference between two points has finite fluctuations, which resemble the ones which occur in the three-dimensional case. The field fluctuations are also rather similar in both cases. The correlations do not have a fast decay. Explicit results are obtained for a solvable model; the fluctuations of the potential are Gaussian with an infinite variance.