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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Bounded fluctuations
- Coulomb systems
- Translation symmetry breaking