01-132 B. Jancovici (Bernard.Jancovici@th.u-psud.fr) and, J. L. Lebowitz (lebowitz@sakharov.rutgers.edu)

Bounded Fluctuations and Translation Symmetry Breaking: A Solvable Model (13K, LaTeX) Apr 3, 01

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Abstract. The variance of the particle number (equivalently the total charge) in a domain of length ${\cal L}$ of a one-component plasma (OCP) on a cylinder of circumference $W$ at the reciprocal temperature $\beta=2$, is shown to remain bounded as ${\cal L} \to \infty$. This exactly solvable system with average density $\rho$ has a measure which is periodic with period $(\rho W)^{-1}$ along the axis of the infinitely long cylinder. This illustrates the connection between bounded variance and periodicity in (quasi) one-dimensional systems \cite{AGL}. When $W \to \infty$ the system approaches the two-dimensional OCP and the variance in a domain $\Lambda$ grows like its perimeter $|\partial \Lambda|$\. In this limit, the system is translation invariant with rapid decay of correlations.

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