Translation Symmetry Breaking in the One-Component Plasma on the Cylinder

Details Translation Symmetry Breaking in the One-Component Plasma on the Cylinder Translation Symmetry Breaking in the One-Component Plasma on the Cylinder

2004-07-14

arxiv.org/abs/cond-mat/0407346v1

J. Stat. Phys. 117 (2004) 159-178

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1023/B:JOSS.0000044066.98352.

The two-dimensional one-component plasma, i.e. the system of point-like charged particles embedded in a homogeneous neutralizing background, is studied on the surface of a cylinder of finite circumference, or equivalently in a semiperiodic strip of finite width. The model has been solved exactly by Choquard et al. at the free-fermion coupling $\Gamma=2$: in the thermodynamic limit of an infinitely long strip, the particle density turns out to be a nonconstant periodic function in space and the system exhibits long-range order of the Wigner-crystal type. The aim of this paper is to describe, qualitatively as well as quantitatively, the crystalline state for a larger set of couplings $\Gamma=2\gamma$ ($\gamma=1,2,...$ a positive integer) when the plasma is mappable onto a one-dimensional fermionic theory. The fermionic formalism, supplemented by some periodicity assumptions, reveals that the density profile results from a hierarchy of Gaussians with a uniform variance but with different amplitudes. The number and spatial positions of these Gaussians within an elementary cell depend on the particular value of $\gamma$. Analytic results are supported by the exact solution at $\gamma=1$ ($\Gamma=2$) and by exact finite-size calculations at $\gamma=2,3$.

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