Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids

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In a Coulomb fluid confined to a domain V, the dielectric susceptibility tensor χᵥ 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 χᵥ predicted by macroscopic electrostatics and gives the finite-size correction term to χᵥ.