Bounded fluctuations and translation symmetry breaking: A solvable model

B. Jancovici, J. L. Lebowitz

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish (US)
Pages (from-to)619-624
Number of pages6
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - May 2001

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Bounded fluctuations
  • Coulomb systems
  • Translation symmetry breaking


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