One-component plasma in 2+ε dimensions

Abstract

The one‐component plasma (ocp) model with neutralizing background is extended to real dimensionality ν=2+ε with −2⩽ε⩽2. The equilibrium properties (pair correlation and thermodynamic functions) investigated within the Debye approximation, up to the second‐order in the plasma parameter e²/k_BTλ^ε_D, with the aid of the Wilson quadratures, interpolate between two‐ and three‐dimensional results for 0<ε<1, and extend the ν=3 behavior to all ν⩽2. The dimensionality ν=2 is shown to play a special role. Quantum diffraction corrections are included in the high temperature limit through a temperature‐dependent effective Coulomb interaction. As a by‐product, the particle diffusion coefficient (Bohm) of the strongly magnetized two‐component plasma taken in the fluid limit may be given a finite volume‐independent expression in the thermodynamic limit when ν=2, provided due attention is paid to the Tauberian properties of the Coulomb potential for −2⩽ε⩽0.