## Abstract

The variance of the particle number (equivalently the total charge) in a domain of length 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 ℒ → χ. This exactly solvable system with average density p has a density profile which is periodic with period (pW)^{-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 → χ the system approaches the two-dimensional OCP and the variance in a domain A grows like its perimeter |∂Λ| In this limit, the system is translation invariant with rapid decay of correlations.

Original language | English (US) |
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Pages (from-to) | 619-624 |

Number of pages | 6 |

Journal | Journal of Statistical Physics |

Volume | 103 |

Issue number | 3-4 |

DOIs | |

State | Published - May 1 2001 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

- Bounded fluctuations
- Coulomb systems
- Translation symmetry breaking