 01132 B. Jancovici (Bernard.Jancovici@th.upsud.fr) and, J. L. Lebowitz (lebowitz@sakharov.rutgers.edu)
 Bounded Fluctuations and Translation Symmetry Breaking: A Solvable Model
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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 onecomponent 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)
onedimensional systems \cite{AGL}. When $W \to \infty$ the system
approaches the twodimensional 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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