Abstract
In a Coulomb fluid confined to a domain V, the dielectric susceptibility tensor χ V depends on the shape of V, even in the thermodynamic V→∞ limit. This paper deals with the classical two-dimensional one-component plasma formulated in an elliptic V-domain, equilibrium statistical mechanics is used. For the dimensionless coupling constant Γ=even positive integer, the mapping of the plasma onto a discrete one-dimensional anticommuting-field theory provides a new sum rule. This sum rule confirms the limiting value of χ V predicted by macroscopic electrostatics and gives a finite-size correction term to χ V.
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Šamaj, L. Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids. Journal of Statistical Physics 100, 949–967 (2000). https://doi.org/10.1023/A:1018779412445
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DOI: https://doi.org/10.1023/A:1018779412445