Debye screening for two-dimensional Coulomb systems at high temperatures

Abstract

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite regionΛ is assumed to be (−Δ_Λ)⁻¹, whereΔ _Λ is the Laplacian with zero boundary conditions onΛ. The hard-core condition is not assumed. The model is set up by separating (−Δ_Λ)⁻¹ into a shortrange part and a long-range part depending on a parameterλ. The self-energies are subtracted only for the short-range part and therefore a choice ofλ is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush “Debye screening,” except that here a modification for the short-range part of the potentials is needed.