Abstract
The variance of the particle number (equivalently the total charge) in a domain of length \(\mathcal{L}\) of a one-component plasma (OCP) on a cylinder of circumference W at the reciprocal temperature β=2, is shown to remain bounded as \(\mathcal{L}\)→∞. This exactly solvable system with average density ρ has a density profile which is periodic with period (ρW)−1 along the axis of the infinitely long cylinder. This illustrates the connection between bounded variance and periodicity in (quasi) one-dimensional systems.(1) When W→∞ the system approaches the two-dimensional OCP and the variance in a domain Λ grows like its perimeter |∂Λ|. In this limit, the system is translation invariant with rapid decay of correlations.
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Jancovici, B., Lebowitz, J.L. Bounded Fluctuations and Translation Symmetry Breaking: A Solvable Model. Journal of Statistical Physics 103, 619–624 (2001). https://doi.org/10.1023/A:1010349517967
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DOI: https://doi.org/10.1023/A:1010349517967