Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids

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 .